BFI stands for "Black Frame Insertion" and it enhances motion resolution in LCD/OLED/Sample and Hold displays by inserting a black frame or blackout between regular frames. This has the result of reducing motion blur by shortening the time each frame is visible, making fast-moving content appear sharper and clearer.
It effectively mimics in a way older CRT monitors, improving the perception of motion. Which for me is huge, because I still game on CRT's on the regular and LCD's abysmal handling of motion is a major detriment to me of my enjoyment of such things, especially for titles that were designed and produced for displays that had much clearer motion.
It's a niche use case i'll admit, and i'd never claim otherwise, and it's not for everybody. But its funny that without that capability, id trade it in for an OLED deck tomorrow.