Luck is chance or happenstance. If something happens from pure good luck, it seemingly came out of nowhere, based only on fate and not on anything you did to make it happen.
If you find a fifty dollar bill on the sidewalk, you might exclaim, "What luck!" Alternately, if you lose all night at the poker table, you'll probably blame it on bad luck. In both examples, you're referring to a mysterious, unpredictable circumstance that affects your life by chance. Luck has a Middle Dutch root, luc, which is a shortened form of gheluc, "happiness or good fortune."