The wireless bridge provides a turn-key wireless network solution. One end (the wireless access point) plugs into a network hub or even directly into a cable/DSL router. The other end (the wireless bridge) plugs into the network jack of a computer, game console, Blu-ray player, or anything else with an Ethernet port. The two pieces have pre-configured encryption already set up, so they instantly have a secure wireless connection without needing to worry about an unsecured wireless network.
As for what that provides for the player, it's the same as running a physical network cable to the player. You get BD-Live, firmware updates via the network, BluTV support (which still had minimal content the last time I checked), and DLNA network support.