What is the WPA, and why won't Mr.Cunningham work for it?

The WPA was an organization implemented by President Roosevelt to assist those without jobs. WPA workers were hired for government projects, which included building roads, bridges, dams, ect.

Cunnigham refused the job because he preferred working his land.

If he held his mouth right, Mr. Cunningham could get a WPA job, but his land would go to ruin if he left it, and he was willing to go hungry to keep his land and vote as he pleased. Mr. Cunningham, said Atticus, came from a set breed of men.