It's providing a usable, enjoyable, natural experience for people using your product. Few people thought consciously about UX until a few decades ago, but nowadays it's realized to be increasingly important, especially for web sites. It's generally synonymous with "usable" or "user-friendly", but it's more gestalty than that. Your web site might be easy to use but still provide a poor user experience by being boring, or slow. Or it might have a lot of bugs, but be friendly and provide good feedback, so the experience isn't bad.
User experience isn't just icing on the cake, but a critical part of our daily life. You can certainly imagine the importance of a usable interface for, say, an airplane cockpit, or those machines that go bing in the hospital. And did you know that poor control room design was the cause of the Three Mile Island incident, too? Beyond that, good UX design is the difference between making our day enjoyable and making it frustrating. And don't we all want a lot fewer frustrated people in the world?
My job is to try to improve the UX of web sites. It's what I enjoy doing. So I can't help noticing other UX blunders in daily life - not just web sites, but offline experiences, too. I started keeping track of them here. We all encounter these, but hopefully my experience in the biz helps me pinpoint them, describe them accurately (and humorously), and suggest viable alternatives. I'll also post any responses I receive from these companies.