In which situations is the word concede used, in which situations is the word admit used, and in which situations is the word accept used?
Concede implies reluctance or a change of mind. "I concede your point" means that I reluctantly accept it, or I go back on my previous opinion and now agree with you. Accept is more neutral; "I accept your point" would be valid if I originally agreed with it, and if I didn't.
Admit (in the context of "I admit your point is true") means to concede something as true, again it implies reluctance. Just in my opinion, it doesn't imply as much of a change of heart as concede does. Admit also has the meaning to confess, as in "I admit I ate all the blancmange, but it was a crime of passion".