A buffer overflow is like filling your gas tank with a burning match on the ground below the fill nozzle. If you put too much gas in the tank it overflows and your car explodes.

Imagine filling your car up with coolant, when you fill it up too much you expect it to fall into the overflow drain, but if you fill it up too fast you can bypass the overflow drain and end up with it making a mess on the engine. You may not know where it will make a mess, sometimes it will end up falling straight through to the ground, or you may end up getting some on your timing belt, but either way, you know you've overfilled your coolant. That's analogous to a buffer overflow.

Now imagine buying 10 gallons of coolant and repeating this experiment until you have a very good idea of exactly how to pour the coolant to make it land on the timing belt, or in other places, and that is a way to think about what happens when a hacker is exploiting a buffer overflow.

:)