Dour describes something sullen, gloomy, or persistent. You might look dour on your way to picking up your last check from the job you just got fired from, and people should get out of your way.
Dour and endure most likely come from the Latin word durus which means "hard." If something is hard to endure for a long enough time, it can make even the most happy-go-lucky person dour. Dour sounds like sour (or closer to "do-er"). It's a tomato/tamahto word, but either way — if you're in a sour mood, you have no sense of humor, and you're dour.