The BSAA are an anti-B.O.W organisation that is famous for being the next stop for series regulars, Chris Redfield and Jill Valentine, along their crusade to battling the many iterations of B.O.W's throughout the series. They have multiple branches across the world, and their series-renown essentially placed BSAA as the equivalent of the ''STARS'' unit for a new generation.
The BSAA are first introduced in Umbrella Chronicles with Chris and Jill leading an assault against Umbrella, and succeeding in the process to finally down the nefarious corporation. For the most part at least; the only remaining founder, Ozwell E. Spencer, was still alive and free somewhere.
Resident Evil 5 then carries the spotlight across Chris Redfield, and the newly introduced Sheva Alomar as they attempt to thwart an arms deal n the African city of Kijuju. Naturally it all goes sour, thanks to the ambush set up by Ricardo Irving - the aforementioned arms dealer they were sent to apprehend. One of BSAA's own benefactors, Tricel, is revealed to be a traitor and is in fact working with Albert Wesker - arch-nemesis of Chris Redfield, to create a new virus titled Uroborus. With the help of fellow BSAA agents, Jill Valentine and Josh Stone, they're able to squash both Wesker's and Tricel's plans. But not with a substantial amount of casualties for the BSAA as well.
The Lost in Nightmares DLC pack would press towards an earlier BSAA skirmish featuring Chris and Jill as they infiltrated the mansion of Ozwell E. Spencer. Unfortunately the duo also encounter Albert Wesker, who easily bests the two. Just as it looks like Wesker is about to kill Chris, Jill makes a noble sacrifice plummeting both her and Wesker out of a window.
The Desperate Escape DLC pack focuses on the team-work of Josh Stone and Jill Valentine as they try to reach Chris and Sheva to give aid. Doug, a BSAA pilot, is also introduced but dies nearing the end just as he picks up Josh and Jill. With Josh taking up piloting duties, he'll manage to reach Chris and Sheva just in time to provide a pair of Rocket-Propelled Launchers, which they use to obliterate Albert Wesker, killing him once and for all.
Resident Evil: Revelations will also act as another pre-Resident Evil 5 BSAA operation, again featuring Chris and Jill, and now introducing the BSAA agent, Parker Luciani.
The BSAA is a highly sophisticated agency with multiple branches across the world, with thousands of operatives, all with Government funding. The most notable members would be Chris Redfield and Jill Valentine, though there are many more introduced through the series, all pertained to their respective branches. Though there are naturally many more members per branch--and many more branches at that--the few that are shown and named for each branch thus far are:
North American Branch
West African Branch