The two most memorable quotes from To Kill a Mockingbird regarding the bird are:
Remember it's a sin to kill a mockingbird.
Mockingbirds don't do one thing but make music for us to enjoy...but sing their hearts out for us. That's why its a sin to kill a mockingbird.
Both of these quotes state the same thing- that the things which bring us happiness and tranquility are important in life.
If one were to consider Boo Radley in the same way as the mockingbird, they could substantiate that he, too, tries to insure happiness (by giving gifts to the children) and tranquility (by protecting them from Bob Ewell).
The relevance of both quotes lies in the fact that the importance of the mockingbird is not known until both Atticus and Miss Maudie tell the children about it. Similarly, the children do not know the importance of Boo either, not until he becomes relevant to the children.