Fiver is most commonly a slang term used to refer to a denomination of currency, most notably;
A five-dollar bill.
A five-pound note.
Fiver is a fictional character -- an intelligent and moody rabbit with premonitions of the future -- in Richard Adams' acclaimed novel Watership Down. Within the story, the author asserts that rabbits "can only count to four", and anything beyond that is simply considered "many" or "a thousand"; Fiver's name came about because he was one of the later (and smaller) rabbits born in a large litter.
Camp Fiver in Poolside, New York, (named after the character) was founded in June of 2000 by philanthropist Tom Tucker to provide a summer haven for inner-city children.
In modern charity circles, the lauded fiver is a person who gives five percent of their income and/or five hours a week of their time to charity -- considered an easier goal than the ten percent tithe the biblical Moses asked for in the book of Deuteronomy.
A math game by the name of Fiver is played on a 5x5 grid with a two-sided counter on each square. Flipping one counter from white to black also flips the counters in surrounding squares according to a set of rules. The challenge of the game is to change all the counters from white to black in the fewest number of moves (and sometimes to deduce what the rules are). Note that this game is distantly related to Conway's Game of Life.