Anything self-indulgent you do for yourself, without thinking about other people. Enjoy a self-indulgent day at the spa! But self-indulgent can also mean “selfish,” like a rambling self-indulgent speech that puts the audience to sleep.
Eating whatever you feel like, even if it's ice cream for breakfast, lunch, and dinner, is self-indulgent. Spending an entire day lying in a hammock when you have a project to work on for school is also self-indulgent. You just do what you feel like doing: in other words, you indulge yourself. Indulge, "to grant as an unearned favor," comes from the Latin indulgere, "be kind, yield, or concede."