When you're a really funny stand-up comedian and you have to pause for many consecutive laugh breaks.
Wow, that comedian is funny! He has been stacking breaks all night.
An old saying in the stand-up comedy world, typically used as a way to brag about how well one did in their stand-up set. Can also be used as a way of casually bragging about how well one does something more generic. Frequently shortened to "stackin'" or "stacking" or "stacked."
Elliott: Mike's killing it up there, he's stacking breaks!
Steve: I fucking stacked tonight, man.