"Stick it to the man" means get back at someone, really give it to him, to take revenge at one's oppression, to call to account etc.
Let's say an employer fires you without a reason, you get upset and say to yourself " I am gonna stick it to the man!". You will sue him, make him accountable for what he has done and in meantime you will make sure he gets what he deserves so he can really feel your anger. :lol: