Means: To be significantly under the influence of alcohol or drugs.
Usage: "I can't read, man, I'm licked", "You were licked last night"
To have something "licked" used to be worth a merit badge, gold star or whatever symbol of educational achievement a school chose to administer. It meant a pupil had done their revision (well, cribbed from the Letts notes) and was confident of acing any test thrown their way. However, to hear the word in class now is to know that your pupils have been staying as far away from their school books as possible, and possibly even the school grounds at lunchtime, meaning as it does to be in a state of some disrepair due to booze, drugs or, most likely, both. If so, not even your most stern but forcefully encouraging plea of "Focus, Nathaniel" is going to do the business.