A full count is when the batter has three balls and two strikes, or a 3-2 count. It is called a full count because neither the number of balls nor the number of strikes can increase without ending the at-bat. Just one more strike would result in a strike out, and just one more ball would result in a walk.
However, a full count does not necessarily mean that the outcome of the at-bat would occur after one more pitch. The batter could foul the ball, and if none of the defensive players catches it, the batter would get another pitch. This could go on for multiple pitches. The batter could also hit the baseball, putting the outcome of the at-bat in the fielders' hands.