You already could read what a neuron is and how it works. What still has to be explained indepth is the way the Action Potential functions.

Neurons send messages via the use of electrochemicals such as neurotransmitters. This means that chemicals cause an electrical signal. These chemicals all have an electrical charge and are called ions. Ions can be either positively or negatively charged, a few examples are: Sodium and Potassium with both an electrical charge of 1+, Calcium 2++ and Chloride 1-. There are also some negatively charged protein molecules.

Remember that opposites attract when it comes to ions, this is how electricity moves through cables.
We saw how each Nerve Cell has a membrane and since it is semi- permeable it will allow some ions through and will block others.

Obviously a neuron is not always firing signals and this is when it's at rest. At this point the inside of the neuron is negative relative to the outside.
Normally the concentrations of different ions would try to balance out on both sides of the membrane, since they would diffuse from areas of higher concentration to areas of lower concentration. But this is where the semi- permeable membrane plays an important role, seeing that it will allow some ions to pass through the ion- channels and other not.

When the neuron is at rest the Potassium Ions K+ can move across the membrane easily whereas the Cloride Ions Cl- and Sodium Ions Na+ can do so less easily. The negative Protein Molecules A- which are inside the neruon can't cross the membrane at all. In addition to these selective Ion- Channels you have a Pump which uses energy to move 3 Sodium Ions out of the neuron for every 2 Potassium Ions it puts in.
When all of these different forces are balanced out, you can measure the difference in voltage between the inside and the outside of the neuron. This is what is refered to as the Action Potential. The resting membrane potential of the a neuron is about -70mV (mV= MilliVolt.) So inside of the neuron is 70mV less than the outside. At rest there are relatively more Sodium Ions outside each neuron and more Potassium Ions inside.