BAMF is an initialism for bad-ass motherfucker — a person who is exceptionally tough, capable, or formidably impressive.
The term functions almost exclusively as praise, applied to someone whose competence or nerve exceeds what a situation called for. Its own origin is undocumented: it is recorded in crowd-sourced references such as Urban Dictionary rather than in traditional lexicography, and it operates as a compressed, printable form of a spoken phrase that long predates the acronym. The abbreviation is what makes it usable — it carries the emphasis of profanity into contexts where the words themselves would not survive.
A separate and unrelated usage exists in comics, where "bamf" is the onomatopoeia for the sound of the Marvel character Nightcrawler teleporting. It debuted with the character in Giant-Size X-Men No. 1 (May 1975), created by writer Len Wein and artist Dave Cockrum, and appeared in Uncanny X-Men No. 94 later that year; it has since become a generic pop-culture sound for teleportation. The two senses share spelling and nothing else, and context reliably distinguishes them.
In my library this is a tag before it is a word. It marks the people whose lives read as proof of the definition rather than as a claim to it — 📝Paul De Gelder chief among them.