BAM is an acronym for big-ass monster in TERA. These monsters are occasionally also called boss monsters or elite monsters. Generally the idea of BAM is formalized meme of MMORPGs, where the bigger the monster is, the more powerful he is.
In early days of TERA there was strict division to boss monsters, normal monsters and minions. Any reference to boss damage, such as "increased damage vs bosses" in weapons or crystals is referring to BAMs or dungeon bosses. Devs seem to have now abandoned this classification. All crystals that affected to only one type of monster are now removed from game, and lately also BAM markers (grey shield or skull icon before name) were removed from monsters names.
This process started when new BAMs where added to reworked Island of Dawn. Unlike real BAMs these monster could be stunned and also some crowd control skills like warrior's Staggering Counter worked on them. Island of Dawn BAMs didn't had BAMs markers either.
Also should be noted that many dungeons have normal-sized monsters in addition of boss monsters. Around level 65 patch all dungeon monsters were marked as bosses, so players can avoid tedious task of constantly switching crystals while fighting them.