Luck is what we wish for, and lucky is what we wish to be. From ancient times, men have tried using specific stones, names, numbers, and even tattoos that they believed would bring them good fortune. These days, universally applicable charms that attract luck and guard against misfortunes, available for sale online or over the phone, is a thriving business that has takers in east and west alike. The ones who seek luck with the greatest zeal, it seems, are the ones who have given it the least thought, and the ones who are most unsure of what they really seek.
Many (if not all) of the results and outcomes in life are probabilistic in nature - at least within the constrains of our limited knowledge and calculation capabilities. For example, there's a very small probability that a person walking on the road will be struck by lightening. So far there's no luck - only probability. However, we consider some of these outcomes as desirable and others as undesirable. If an event that is desirable to me happens in spite of lower probability, I call it (good) luck (or say I'm lucky). If an undesirable outcome that actually had a very less chance happens, I call it bad luck. So an example of bad luck would be to be struck by lightening, and at least some may think themselves lucky if their mortal enemy were the one to be electrocuted!
If we had complete knowledge about the state of the atmosphere and the ability to precisely calculate when and where lightening will strike based on the current state and laws of physics, then there would be less of probability and so lesser attribution to luck. (But even there, the Principle of Uncertainty leaves some room for chance). So, arguably, scientific advancement and knowledge push more events from the realm of luck into the realm of predictable physical phenomenon. From my philosophical perspective, I believe in Karma - the universal law of cause and effect, by which every outcome has a cause whether or not we know about it. So in this case, luck is the result of a cause that we do not know about.
In short, luck is our way of summing up the desirability of unpredictable events that occur in our life!
I originally expressed these thoughts in response to a question on quora and then thought it was worth sharing with a larger audience.