Tom Robinson is one of the symbolic human mockingbirds of To Kill a Mockingbird. Along with most of the children in the story--particularly Jem, Scout and Dill--Tom (and Boo) fit the description of the songbird that Miss Maudie describes to Scout.
Mockingbirds don't do one thing but make music for us to enjoy. They don't eat up people's gardens, don't nest in corncribs, they don't do one thing but sing their hearts out for us. That's why it's a sin to kill a mockingbird.
The mockingbird represents innocence and sweetness, childlike attributes that can also be found in Tom and Boo. Tom is an honest and hard-working married man who comes to Mayella's aid out of sympathy for her. Poor and crippled, he is a sympathetic character even before he is unjustly accused of raping Mayella. When he is found guilty, things seem bad for Tom; but when he is murdered, he becomes even more symbolic of the mockingbird: Innocent of anything but trying to make people happy, Tom suffers the fate that Miss Maudie warns Scout about.