Definition of check/fold
An check/fold is when you check with the intent of fold versus any bet. You can check/fold for many reasons. You can check/fold because your hand is mediocre or because the pot is multiway and your hand is too weak. Imagine that you have a 3bet hand like JJ, but you have received 4 calls. The flop falls A-K-2 all in heart and you don't have the jack of hearts. This is a moment where you think one move ahead and think that this is the ideal situation for check/fold.
Another reason for check/fold
There is no need to be afraid of check/fold. Some players are too proud to do so. If you've made a 3bet with 9-T in spades from the small blind against a button that opens too much and the flop isn't favorable and you're up against a calling-station player who never folds, rather than losing your entire stack trying to bluff him with limited success, maybe you should just tell yourself that it's simply time for check/fold. In poker, you make money making calls, but you also save money making folds.