Definition, n. Colloquialism of the American South, Appalachia
This is one of those southern colloquialisms or turns of phrase that, if you grew up there, its meaning is as natural as breathing, but when confronted with having to explain it to an outsider, you find that it requires a solid paragraph of explanation.
It takes it associative cue from the American Pileated ("Red Headed") Woodpecker. I guess it was thought that pounding your head against a tree all day long was stupid. It may be borrowing on the "redheaded" thing as well - as in "I'm going to beat you like a red headed stepchild." It is, according to the etymological research I've done, at least as old as the American Civil War. Still, it's always seemed like something of a mystery - not literal at all. Yet, growing up with it, the meaning is crystal clear.
The term is pejorative, applied to poor or ill-mannered whites. It is similar to white trash, yet carries more of a connotation of stupidity and baseness. If the label of "white trash" conjures up images of poverty and undereducation, peckerwood adds a measure of extra viciousness and stupidity. There are shade of pissant here as well - somebody who is a nuisance and not worth the time it takes to deal with them. I would not say, however, that it has the same negative strength as "cracker", which carries a powerful connotation of racial hostility.
It can be used jokingly,"What's up peckerwood?" It can be dismissive, "I've got better things to do that waste the afternoon chasing down those peckerwoods." In the correct context, with sufficiently hostile inflection, it is a fighting word - "What did you say to me, you sawed off little peckerwood?."