Falcone was a pool shark who played out of a local pool hall. After Dylan McKay had been playing there for weeks, Falcone was looking for Dylan because his game was getting good and he wanted to play him as mentioned by the bartender that worked there.
The first time they played, Dylan won five hundred dollars off of him. However, the next game he played him drunk and Falcone lamented to Brandon Walsh that he had already won his money back. Dylan refused to yield despite multiple losses and Brandon's warnings, so Dylan kept losing and lost eight hundred dollars. He didn't have the money, so Falcone and his friends laid a beating on Dylan while restraining a horrified Brandon.
Dylan later mentioned that he was going to pay Falcone back his money and it was assumed that he did since Falcone was never mentioned on the show again.