Like most games, golf presents the challenge of mastering particular skills and improving one's performance. It also provides some physical exercise appropriate for my age, the chance to get outdoors and enjoy nature, and the opportunity to meet new people.
Additionally, it's a sport I can enjoy with my wife. Neither one of us is very good at it (my best score on a full-size course is 101), but we love to get out and play a round on the weekends. (We also love to play around on the weekends, but that's a different sport.)