BBEG stands for Big Bad Evil Guy. It is a category used to cover climactic endgame bosses or story-driven foes. They are high-powered, high-level, and not to be challenged by anyone, save the most prepared and tactical parties of adventurers.
As the action economy is quickly unbalanced in the BBEG's favor, any good DM will empty the barrel of tricks and traps at their disposal for these encounters; environmental hazards, powerful minions, nasty traps, inventive mechanics to overcome them, and a fat sack of hitpoints to make sure the combat doesn't end too soon are all on the pregame checklist. All that complicated combat aside, remember that the act overcoming the BBEG will change the nature of the world, of the PCs, and the story's emotional trajectory. Be open and honest, let the dice guide your way, and prepare for a late night, because these sessions run LONG.
