In "To Kill a Mockingbird," what is the implication of Mr. Gilmer calling Tom a boy and why is Dill the one who gets upset by this?

Dill is upset when Mr. Gilmer calls Tom "boy" because Dill realizes this is a disrespectful term.  Tom has admitted that he helped Mayella because he felt sorry for her.  In the deep south in the 1930's, whites did not feel that blacks could feel sorry for a white person.  Whites felt that any white had an immediate advantage over any black person simply be being white.  For Tom to admit he felt sorry for Mayella implied that he felt himself to be in a better position than her.  Mr. Gilmer, in order to reduce Tom to a lower level and to put Tom in what Mr. Gilmer and most of the all-white jury would consider "his place", Gilmer uses the word "boy".  This word takes away Tom's identity as a grown man; as an adult.  "Boy" was frequently used by ignorant whites when referring to black men for this reason.

Dill is the one who gets upset because he realizes that the term is disprespectful.  He knows that Tom was simply trying to do a good deed for someone and that Tom should be thanked, not punished, for his actions.