In Harper Lee's To Kill a Mockingbird, Atticus' comment comes in Chapter Eight. This is the first time Scout has ever seen snow, and she and Jem make a snowman, with a mixture of some snow and a lot of mud. The kids are very anxious that Atticus see their creation when he comes home from work. Atticus says:
Son, I can't tell what you're going to be—an engineer, a lawyer, or a portrait painter. You've perpetuated a near libel here in the front yard. We've got to disguise this fellow.
To comprehend the quote's significance, we need to know the meaning of the words "perpetuate" and "libel." "Perpetuate" is used as a verb here; it means...
...to cause to last indefinitely.
The other word of note is "libel" which means...
...a written or oral defamatory statement or representation that conveys an unjustly unfavorable impression.
What Atticus has told Jem with his statement is that his snowman looks very much like Mr. Avery, something the kids had already noticed, as Scout pointed out...
Mr. Avery's sort of shaped like a snowman, ain't he?
Atticus' notion that the snowman looks so much like Mr. Avery has already been expressed, again by Scout:
"It's lovely, Jem," I said, "Looks almost like he'd talk to you."
Looking like Mr. Avery might not be such a bad thing, but Jem uses small pieces of wood for facial features, so that...
Jem succeeded in making Mr. Avery look cross.
And it may be for this specific reason that Atticus suggests that they change the snowman's appearance so that Mr. Avery is not offended. When Atticus states that Jem has "perpetuated a near libel," he is in a sense congratulating his son on the likeness of the man that Jem has captured in the snow-and-mud figure. It looks very much like Mr. Avery—but it is unflattering to him—and Mr. Avery might feel the caricature creates an "unfavorable impression." In the broadest sense, committing libel, or insulting someone's reputation beyond repair, is a criminal offense.
Basically, Jem shows a remarkable talent for creating a figure that looks very much like Mr. Avery, who might not appreciate the snowman's likeness to him.