A "burn" in the '70s was about the same as a "diss" today, except that today, we don't point them out. To shout, "Burn!" at someone would mean that either you or someone else got that person good, either by fooling them, humiliating them, or making them the butt of a joke. This was exemplified on That 70s Show, when Eric's grandmother dropped a passve-aggressive bomb on Eric's friend, causing Eric to say, "That, my friend, is the seldom-heard, but much-feared 'Grandma burn'."
I went into grandma's closet to find something, and I saw the holiday outfit I got her that she said she loved was shoved in a box by the ceiling, and never worn.