The giant coin, like the rest of the items in the 'Cave (excepting those directly related to Batman's work) are trophies from notable cases Batman has worked.
In the Animated Series, the Giant Penny is part of a death trap Batman was once subjected to by Two-Face. Batman was tied to it, and Two-Face triggered a giant coin flipper. He intended it to crush Batman (if it landed bat-side down) or to have the impact shatter his bones (bat-side up). Batman got himself loose mid-air, and foiled the caper.
In the comics, the Giant Penny is a trophy of his defeat of Joe Coyne, who committed penny-themed crimes.