Jeremy Fisk is a detective with the NYPD's Intelligence Division.
That department is "a well-funded anti-terror unit modeled upon the CIA—suspects that the event might also be a warning sign that another, potentially more extraordinary scheme has been set in motion. Fluent in Arabic and the ways of his opponents, Fisk is a rule breaker who follows his gut—even if it means defying those above him in the department’s food chain."
I was quoting that passage because it really says a lot about the series and the character. Fisk is a veteran cop who is smart and, more importantly, realistic. He routinely sees things as they are and not as he would want them to be, a mistake the bosses he often has to work for make more than once. Being a good team member, though he would rather work alone, he points out deficiencies in Plan A and that does not always (read ever) sit well.
In one of the books, Fisk states that he is "an elite cop, or trying to be." He goes on to say in explaining why he is a cop and why he keeps going after the bad guys, "I think the people of New York City will be better off with me inside the department than outside of it." No arrogance, just a belief that he is doing something he is good at and that is worthwhile.
Fisk is unmarried. I can find no evidence that he ever was but information on Fisk's background is not readily available. The recorded adventures very much live in the now so the best we can discern is that Fisk is in his mid-to-late 30s and has been in the policeman business for a fair number of years, loves it, hates the bad guys, and would not want to do anything else.
He also loves New York City and has little good to say for any part of the state that isn't in the metropolis.