For the most part agree and concur are synonyms, although concur has other usages that are apart from the meaning of agree. There are however some subtle differences, that arise, and only shows up in certain circumstances.
Let me give you an example:
CEO: "You will agree to sign this letter of resignation or I will press charges."
Chairman: "I concur!"
Employee: "I do not agree."
The CEO cannot say, "You will concur to sign ..."
The chairman can also say "I agree", however he would come across as being a subordinate to CEO's directive, whereas he's actually ratifying it.
The employee, on the other hand, cannot really use the phrases I concur or I do not concur because they sounds odd in adverserial situation as a direct statement.
However, if the employee wanted to be dry about it he could say,
"I do not concur! but I agree because I really don't like jail food"
I wonder if this helps :-)