Warning Spoilers!

There are two ways to interpret this topic, mainly because the TV series had a different portrayal of the project than the movie. The TV series focused the HIP as a psychological gain. "All things return to mother" as Gendou stated, or a "return to nothingness" as Ritsuko said. Although the topic in it self was debated amongst the characters, Shinji in the end figures it out. A Self actualization. Some would call it a brain washing...but in terms of the story it was a revelation in one's self, building "your" world with the aid of others, thus the word instrumentality. Using others to survive, or as Kaoru said, "You lilims use the instrumentality of those [eva's & others] to survive." Shinji in the end creates the world he wants to live in. The whole thing is psychological.

Theories
Yes there are multiple theories, why? People just can't agree on one thing, I think all these answers are true...
The whole darn thing was thought up in Shinji's head, that what we see in the end was reality but he just could not come to terms with it, so he created this world where he could be special... in some weird way. That's the explanation for the constant reference to his walkman (SDAT player), notice that it always plays from 25 to 26 then 26 to 25...well there are 26 episodes in EVA and most people believe that when he is alone he is escaping, and trying to reach the end of the series to get away from all the horrors so he may be happy like he was in the end. Another reason is this: In the last episodes (25, 26) he, like I mentioned, goes into this self actualization, where he tries to discover himself. Well, it could be that the last two episodes is what's going on in his head while he's listening to the SDAT. Get it?

It could be Anno's ( the creator and director ) personal opinion and overview of the whole thing. If anyone knows a little about Anno, they know that the guy has had some problems in life. The series is a reflection of his life. The last two episodes can be interpreted as a reason to make EVA or why he made EVA. If you read the scripts and change some of the words around, it seems like Anno is talking to himself. For example: Shinji says, "Why pilot eva?", it could be translated as Anno says, "Why make EVA?" Shinji says, "because I am praised when I pilot eva." Well this in turn can be translated as Anno: "Because people praise me when I make EVA."

FACT: Movie Since the series continues with the movie, this is obviously the real answer. It's very simple. The human species has reached their evolutionary limit, Seele wants to further extend the evolution phase of human beings, to do this they need a clean slate. It was first thought that the Third Impact was going to destroy the whole world, but in fact the Third Impact was a merging of all life on the planet. So in fact the theory behind the TV series stays true with all elements returning to mother as stated by Gendou, which in this case IS Lilith. Lilith joined with Rei and together they formed a huge white glowing being, no it is not the being we perceived as Adam, but instead it is something we all can recognize, a huge Rei. This was Gendou's attempt to conduct the 3rd, stopping Seele and using Rei. Anyway I know it sounds weird but it is true. In the mean time Unit-01 and Units 5-13 who were all combined in the form of the tree of life (which someday soon I'll have time to decipher) which I believe is Seele's attempt at artificially creating the 3rd. I dunno something crazy happens with Unit-01 and she (it?) refuses to finish HIP, things go nuts and big white Rei dizzolves and next thing you know all that is left of the world is Shinji and Asuka (possibly the new Adam and Eve, or in this case Adamo et Eva) who is bandaged up just like we saw Rei, Eye patch and broken arm. Do I see something fishy about this...hmmmm.

So all in all BOTH TV and Movie come together...The next human evolution phase was the combining of all people. In this state, the people themselves are their own god. We got to see a glimpse of what some of the other characters created. Now the Question is..."Was what we saw with Shinji and Asuka the REALITY or Shinji's world? After all Asuka dies fighting the Eva's.

In Addition: Ok here is the updated part of HIP. I'm going to try to clear things up as best as I can. Human's have reached their evolutionary point. Heck I'll even give you the actual dialogue...er translated.

• Misato : "The Human Instrumentality Project" makes mankind, who has already come to an evolutionary deadlock, a failure for existence. It's just a dream world. The commission will still use the Evas, but get rid of Adam and Nerv, it was just as Kaji-kun expected.

Basically humans have reached their evolutionary limit. HIP is actually a dreamworld where everyone creates their own destiny.

Side Note:
It's kinda funny how Anno changed the ending...I mean in the TV series he had Shinji create this really cool world where him and Asuka are childhood friends and Rei actually has a beaming personality. Gendou is not such a dick, he's actually kinda funny...and Yui is so motherly...*sigh* BUT now we're stuck with this funky ending where Shinji and Asuka are left alone. Kinda makes you wonder what was goin through Shinji's head when he decided what world he wanted...after all he does have control. But then again...what was the real ending? I mean Anno stuck in those last two eps and removed the actual last two which will be re-released as OAV's. And ADV is gooing to release them as the endings for EVA here and pull out the last two that aired in Japan. Wha??????

Source: Movie and TV series

Update
THEORY I've been getting a lot of theories on the impacts so I think I'll cut clear on what I think. There has been a lot of talk that there are actually different kinds of HIP and Impacts, a destructive and constructive one. I really don't agree. I think the Impacts were caused by man and NOT by the Angels. Even Misato said so (see above). The HIP is also a by product of man and not a result of the Angels coming into contact, thus the term "HUMAN Instrumentality Project." I think the only reason really of the Angels coming down is to take Lilith back, not destroy mankind. Mankind is the one who wants to destroy itself. The destruction of the 2nd Impact was from trying to capture and shrink Adam. When Kaoru is sent he hiimself doesn't really understand, he is constantly discussing with himself what he must do, I think he was misinformed by Seele...HA that's it, Seele and everyone else had the wrong idea about Adam, except for Gendou. Gendou was the only one who knew that Adam was useless for HIP because all things return to Lilith and not Adam, even Kaoru himself realized that, he thought he was looking for Adam, but found Lilith instead. The only reason why Kaoru didn't want to join Lilith was because he was sent with the intention taking mankind with him, he was sent with the intent of completing HIP as planned by Seele. See Gendou knew all this which is why he created Rei. Kaoru was for Seele, and Rei was for Gendou. Kaoru failed and the Eva Units-05 through 13 were sent in to complete the task along with Eva Unit-01.

• If Kaoru was successful, Seele would control HIP.
• If Rei was successful, Gendou would control HIP.
• But Shinji succeeded and thus controlled HIP for the fate of the world as seen in EoE. (The TV HIP is totally different from the movies)

Ok so I side tracked a little, but here is my conclusion. 2nd Impact resulted from the contact/encounter with Adam. There is no 3rd Impact. It's just a story to scare people or make some simple excuse, "National Security" you could say. Instead what 3rd Impact really is, is HIP.

And please don't give me that Bull Sh!t about "returning to Adam" and what not because it makes no sense. Eva is a clone of Adam. Many times Angels have come into contact with Eva, and nothing happened, Angels at times even assimilatied with Eva, and, "gee, gosh darn it" the world is still around. Heck here's proof! When Gendou ordered Rei to get the Lance I believe it was Misato that freaked out and then realized that impact wasn't going to happen. Although it could because technically it was Lilith, but taking the ignorance of Misato and her limited idea of Adam having the lance, she still figured it wouldn't happen with Adam.

Well what about Kaoru saying all things must return to Adam. Well look at it this way. First you have to believe that Kaoru was raised and sent by Seele, if you don't follow that then my theory is invalid to you. I believe that there was a misinterpretation of the Dead Sea Scrolls, then that's where Kaoru's revevlation makes sense, all things return to MOTHER.

Source: Movie and TV series

Reader Theories:

• My personal opinion on HIp is the TV ending is where Shinji has accepted the Complement whereas the EOE is the version where Shinji rejects the Complement. In other owrds, TV is the happy ending while the movie is the sad ending.
  -GundamDendrobiumGP-03S
• Theory about the Third Impact: There are actually two possible Third Impacts. A destructive one (annihilation of mankind) would occur if an angel came into contact with Adam. Hence when Kaworu says that if he lives (returns to Adam) then mankind will perish. After that, he realizes it is Lilith. If an angel were to merge with Lilith, however, there would be a constructive Third Impact. All of mankind would leave their bodies behind and merge into one great being. This is what Gendou wants. I think this is why Lilith is semi-readily accessible in Terminal Dogma while Adam is hidden somewhere else.
  -pepper
• The third impact can be caused in three ways with two. the first is an Angel coming in contact with Adam this will cause the destructive third impact and cause the human race to die. The second is for man to defeat all 17 angels, create a man made angel to meld with lilith and to have the lance. this will cause the constructive third impact and man will become one being who will go to heaven. the third way is to have one of the 17 angels to come in contact with lilith. This allows man to become one being and go to heaven. Before you say why did NERV try to stop the angels well for Gendo to complete the impact the way he wanted Rei would have to meld with lilith. SEELE really didn't care if it was an angel or rei that came in contact with lilith but they got tired of waiting so they decided to send the 17th angel so the third impact would begin. the angels cam towards NERV because they believed that Adam was there and he was. They had did not want to meld with lilith be! cause that would defeat their purpose of preventing humanity from reaching Keter and the third impact
  -Angela