Mr. Avery is a neighbor of the Finches who whittles wood. He is rather coarse person, one time blaming the children for the bad weather because , he says, disobedient children make the seasons change. Nevertheless, he risks his own life fighting the fire at Miss Maudie's house.
He has more of a "claim for fame". He is a frugal man and he is not the best person, but he tries to help Miss Maudie by fighting the fire in her house. One time the kids were on the street and they thought he must drink a lot because he was going to the bathroom in public.
If this is a question from your teacher, and he/she is a bit of a trickster-Mr. Avery has another "claim to fame," from Scout and Jem's viewpoint. For Mr. Avery's not-so-gallant claim to fame, check out the beginning of Chapter 6. Within the first page of the chapter Scout mentions that, "Besides making change in the collection plat every Sunday..." which means he's a bit cheap or frugal. Reading a little bit further there is something even more shocking that he does, "...but a closer inspection revealed an arc of water descending from the leaves and splashing in the yellow circle of the street light...Dill said he must drink a gallon a day..." Basically, the kids caught Mr. Avery taking a bathroom break over the edge of his porch--pretty impressive!