What does humor-challenged mean?

It must describe someone who lacks a sense of humour. Humour is a big challenge for such people: they struggle to see that anything is funny. Such phrases were quite popular a few years ago. Someone short would be called vertically challenged, someone fat would be called circumferentially challenged and so on.

It means they lack a sense of humor, being a play on the phrase "mentally challenged", which is one polite way of indicating mental retardation.

The idea behind being "xxxx challenged" is that you struggle personally with "xxxx". It's a more polite way of mentioning it because it supposedly gives more dignity to the person. There is a hope of rising above the challenge (as in mentally challenged) vs. something labelled as an "inability" or "handicap".

However, some find the "xxxx challenged" terms patronizing.

The humor behind "humor-challenged" is that it is patronizing in the same way. It can be used kindly to say, "Don't worry you'll figure out the joke at some point." But, I've also heard it used to mean that they think you have an inability to understand any kind of humor.

It generally means that they have trouble recognizing irony, and double meanings. Depending on the context it can also mean that the person lacks a sense of humor in general, as Barry said.