Basically it works like this. Your battery holds electricity, when you turn the key (which is a switch) it routes the electricity from the battery to the starter solenoid and then to the starter which starts the engine by using gears to make the engine components move until their is combustion which uses the power generated from the fuel to continue to make the engine run. At that point, the battery isn't used at all, the alternator takes over to supply the electricity needed to power all the electrical components AND recharge the battery for the next time you need to start the engine.
So, there could be a couple things wrong. I'll go in order of least expensive to check and/or replace (typically, but it varies from car to car).
1) Dead/Low powered battery. Solution, have autozone test it to see if it's good. Or have someone give you a jump if it starts then you know the battery was dead/low. Dead means that it won't hold a charge anymore, low means that either it was drained by something being left on or the alternator isn't charging it properly.
2) Bad solenoid.
3) Bad alternator. Can also be checked at Autozone, but it might need to be removed to test. This will also help to be determined if the batter is good but doesn't have any power.
4) Starter. This too can be tested at autozone after it is removed. They do wear out so not uncommon for them to go bad.
Hope this give you a better understanding of the potential problems.