Kagome Higurashi is just a normal junior high school student who lives at a shrine with her mother, brother, and grandfather...or so she thinks. Actually, she is this amazing 15 year old girl with special powers.
We first see her in Episode 1 chatting with her grandfather about her 15th birthday, when he gives her some weird looking mummified hand. Anyway, she first realizes that she has special powers when she was grabbed by a centipede youkai and taken through the Bone-Eaters Well back to the Feudal Era.
Here is where she meets Inuyasha for the first time. Though, he is sealed up by a spirit arrow on the god tree, Kagome can't resist going to check it out, and rub his strange ears. That's when she is found by a few villager's who think that she's trying to unseal Inuyasha.
Well, to avoid telling you the whole story and ruin it for those who haven't seen it yet, I'm just going to stick to the basics for now. Kagome is the reicarnation of the powerful Miko (priestess) Kikyo who has the ability to purify the Shikon no Tama. When Kikyo died, the Shikon no Tama was burned with her remains and by some fortunate/unfortunate chance, was replaced inside of Kagome's body.
Anyway, Kagome teams up with Inuyasha, after the Shikon no Tama was shattered, to find the shards because she is, so far, the only one who can see the them. If Inuyasha misbehaves, all she has to do is give the command "Osuwari!" (sit) and hilarity ensue's! Though they seem to be the most unlikely pair, Kagome is able to keep up with Inuyasha regardless of what he does to upset her.