The Breakout is the first moments after you break the surface of the water when pushing off the wall. Essentially the first few strokes off the wall.
Having a strong breakout is very important in sprint races and is often practiced during sprint sets. For example:
4 x 50s @ 1:00 Freestyle - "Fast breakouts"
Means to do your first three strokes off of each wall very fast, but swim more relaxed/moderate the rest of the length. Pretend you are racing to the 12.5 meter mark!