Answer:
Mr. Gilmer used the term in a derogatory and demeaning manner to show his superior authority over the black man. He also used the word to imply that Tom means little in the community, and thus led him to believe his inferiority among the people.
Explanation:
Mr Gilmer is the lead prosecutor in the Tom Robinson ra pe case in Harper Lee's To Kill A Mockingbird. He is a white man, who also uses his language to demean and lower Tom's face in front of the whole jury and the people witnessing the court scene.
By calling Tom and constantly addressing him as "boy", Mr. Gilmer is using his position as lead prosecutor and also sees himself as the voice of the Southern white folk in the packed room. Tom, being a black man, is seen inferior to the whites, and taken as guilty even before any proof of evidence can be presented.
Chapter 19 of the book shows the court scene where Mr.Gilmer repeatedly called him "boy".
"Had your eye on her a long time, hadn’t you, boy?"
“Then you were mighty polite to do all that chopping and hauling for her, weren’t you, boy?”
“With Mr. Ewell and seven children on the place, boy?”
“You did all this chopping and work from sheer goodness, boy?”
This constant referring to the use of the word "boy" is meant to demean his status and power over the grown man. Despite being an adult, his blackness seems to signal his inferiority, his lower status in the community. The word is also used as a means to prove their power and authority over him, leading him to fear them and thus, be submissive to whatever they ruled.