I think its introduced on the 3rd night; foxy hides in the cove, and you have to check the cove very frequently so foxy doesn't come out. When it does come out it runs down the corridor and gives you very little/no time to close the door on it.
The first few nights nothing really happens, but, it gets more tense the more nights happen. There are actually 7 nights in total and the 7th is a custom night where you get to pick how hard each of the characters are.
Very interesting concept and gameplay mechanics