The humor is largely self-deprecating jokes about the South, "rednecks", and themselves as bumbling husbands/fathers/men in general. They proudly run with Southern stereotypes that the rest of America has been cracking wise about for decades (and sometimes still is). For instance, rather than refuting the concept of "The Redneck", Jeff Foxworthy defines him as someone with "a glorious absence of sophistication", and he means that as a good thing.
The four men enjoy successful stand-up careers, Foxworthy is the highest-selling comedian of all time, and they've shot three successful films named, The Blue-Collar Comedy Tour. There was also a short-lived TV show called Blue Collar TV, a sketch show based on their humor. It was a huge hit (by the now-defunct WB network standards, anyway) for about a month, then it fell to the basement of the ratings.
Also has a Spiritual Successor of its own in "Them Idiots", who are made up of Jeff, Larry, and Bill (Ron having distanced himself as his comedy is dirtier and doesn't cover southern humor as much as the others).