
Basically the Mini Ball was smaller and could be dropped down into the barrel. When the gun was fired, gases expanded the base of the ball, allowing it to travel down the grooves of the gun. This allowed the gun to fire more accurately, and be reloaded more quicly.
This allowed soldiers in the civil war to kill eachother a lot more efficiently. Which is both a good and a bad thing. This is just one more invention by man to make kililng eachother easier.