When grapes or grape bits are left in a fermentation vessel, as in red wine making, all the solids—grape skins, seeds, stems, pulp—rise to the surface. This mass of solid matter is called a "cap," and winemakers want to integrate the cap back into the wine. Think of the cap like a tea bag—if it's just sitting there floating on top, you're not going to get the color or flavor that you would if you dunk it in to steep. (Also, leaving the cap floating on top runs the risk of bacterial growth.)
There are two main ways to deal with the cap: pump-overs and punch-downs. Pump-overs are what they sound like: the fermenting juice is circulated, or pumped, over the cap. This doesn't break up the cap so much as it helps keep it submerged. A punch-down is when a device (think of a big potato-masher) pushes the cap down, breaks it up and submerges it again.
The how (and how often) of dealing with the cap depends on a winemaker's style. The more aggressive one is with breaking up the cap, the more a wine will be extracted, dark and tannic.
Just an FYI: if a winemaker invites you to help with a punch-down, you're in for a workout! It takes an extraordinary amount of physical effort to punch down that cap. (YOU CAN SEE PAUL IN ACTION IN THIS VIDEO)