It means to be sort of serious when telling a joke and only little parts (if I may) are understood by the listener. It requires work, actually, for the listener to completely get it. It also means you're very humorous. So basicly, a "dry" sense of humor is a good thing.
2nd Answer:
But the question was, "What word" . . . the word could be "droll".
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The definition of the word droll is an interesting way that provokes a bland sense of entertainment. It generally means that dry humor is being used in the situation.
I have a naughty sense of humor. It can be called sarcasm or a dry wit. I love shocking people with lewd comments. I like naughty jokes, too.
It basically means that your humor is either sarcastic or when you say things it almost doesn't sound like it was meant to be funny but it is. In other words, if you say something that sounds serious by the tone of your voice but actually ends up being funny, you're practicing dry humor. Of course a lot of people don't get this type of humor, because it's not as obvious. A good example of dry humor is the movie "Napoleon Dynamite".
"WRY" is an adjective, which describes something Use it to describe something or someone that is unusual, contrary, distorted, devious, perverse, ironic, etc. Example: "His remark about my chances of winning the contest was wry and sarcastic."
Drought