- For the current list of changes and new features active in the PBE, see: VPBE.
The Public Beta Environment (or PBE) is a "test-centric" server on which upcoming patches are available for public testing. This allows Riot Games to fix any bugs before the patch is released to the rest of the world. Players can test new champions and features before they are publicly released. This is an invaluable resource for Riot, as public testing saves time and resources as well as providing fun new opportunities for players.
Additionally, players on the PBE have their RP reset to 8000 every day. This allows players to purchase and use any champion, skin, or other feature in the game on the testing servers. While not necessarily for what the PBE was intended, this allows players to try out champions and skins before buying them on their actual accounts. This can be a valuable tool in making a well-informed purchase that the player won't regret. Players can report bugs at any moment. 
Main information post: Useful information for new PBE players
PBE Community: PBE Board