To enrich something is to make it richer, or to improve the quality of it. You play the lottery because it might enrich your bank account; you play ping-pong to enrich your quality of life.
Regardless of the sense it is used in, the key to enrich is the word rich (you can almost think of it as the verb form of the adjective). So to enrich something is to make it rich, richer, or just plain better. Enrich always needs an object: You can’t visit a wax museum just to enrich, but you can go to enrich your life. Verbs that enrich include improve, enhance, cultivate, better, and develop.