It can also mean that something is hot and it is scorching your fingers or leaving a red mark.
Without the S it can be a diss to some people. Or the same thing as what definition 2 was just non-plurial.
EG #2. Ouch! The kettle's hot! It really burns my fingers!!!!
Shaggy: *eats scooby's sandwich*
Scooby-Doo: Where could my sandwich have gone? It was just here 2 seconds ago!
Scooby-Doo: You ate it!
Shaggy: :) HeHe.
(2) slang: to smoke marijuana or any other drug used with fire, to get high. see burn out
(3) verb: to char or scorch something using fire
Child: Oh, BURN!
(2) Stoner 1: Man, are we gonna get burnt out today?
Stoner 2: I don't know, it isn't 420
(3) Tony watched the logs burn in the fire.