It depends a bit on the institution, but in general, night float consists of a resident working during the night (5 PM to 7 AM, 5 days per week) to cover patients while the day teams are at home sleeping. Many programs (in many different specialties) have residents do this for a couple months during the year.
Its shift work as opposed to call. Someone works days and another...the "night float"...works the night shift. Generally they cover multiple services and patients that they don't know so that for every 1 night float in the hospital several services can do away with call. there is more signout (ideally) or if the patient load is to heavy they just do away with signout all together and nobody in the hospital knows what is going on with the patients. Many people like it, some don't.