If I understand it correctly, a contingency fund or account is a budgeted amount intended to cover unplanned costs. It is rather like insurance. You set some extra money aside, in case someone spills coffee in the copy machine, or you get a rush job and need to hire a temporary worker, or the price of heating oil suddenly goes up, or....
Web examples:
"the Board intended to create a 'contingency account' ... 'to assist other entities' and 'respond effectively to any unexpected needs as they arise...'"
"...contingency fund to cover potential misestimates and unforeseeable events"