The power supply is the part of the computer that you plug into the wall to give your computer power. The power supply converts AC (alternating current) to DC (direct current).
Each voltage output circuit is called a rail. Newer power supplies have multiple rails to avoid overloading one circuit. The rails will help you distribute power between multiple circuits much like a circuit breaker in a house.
Power supplies are ratting in watts. The watts tell you how much power can be supplied to the different parts in your computer. The more devices that are in your computer the more watts you will need.
This is how well your computer manages its power. The 80 certification lets you know how efficient the energy uses is. The 80 certifications that are out now are Bronze, Silver, and Gold, A platinum certification is going to be out in the future also.
Having a modular power supply means that you only need to plug in cables that you are using. These are generally more expensive then non-modular power supplies. Modular power supplies are better for help manage air-flow inside your case.
Thats some basic info on power supplies
If you have any questions please leave them in the comments and i will answer them.