BFS stands for Bait Finesse System. This is a technique originating in Japan. Fisheries in Japan have more anglers than accessible waters -- freshwater. This creates highly pressured environments for anglers in Japan.
Japanese anglers learned those using finesse baits had more success of catching while other anglers were only fishing. There are many types of finesse systems with the most well known being spinning finesse, fly fishing, Tenkara, and now BFS.
The easiest way to think about BFS is it's an ultralight baitcasting setup. This is by far, the fastest growing segment in fishing in the US. If you watch professional bass anglers, they usually have at least 1 spinning setup in a swarm of baitcasting gear. They use the spinning setup for throwing more finesse presentations (lightweight or ultralight baits) when the bite gets tough. These finesse baits aren't effectively castable with traditional baitcasting reels. Anglers can now put their spinning gear aside for BFS.
Think of BFS baitcasting reels as 50-series or 500-series spinning reel. Traditional baitcasting reels are usually 100 to 300-series for bass and can be much larger for large game fish. BFS reels are easily identifiable by their shallow spool. BFS reels are usually spooled with only 50m (164ft) of ultra thin line.