A hitch is an obstacle or hindrance. You might be late because of a last minute hitch, like waiting for a family of ducks to cross the road. If things go well, they go off without a hitch.
The word hitch has a gazillion meanings — it’s a hook, a limp, short for hitchhiking, slang for getting married — but the most common meaning is that a hitch is a little problem. If you’ve packed a picnic and then it rains, the weather is a hitch in your plans. Hitches include hang-ups, snafus, impediments, and other things that interfere. Often this term is used in the phrase "without a hitch" for things that go smoothly.