Self indulgence is often referred to someone who is being greedy, or is selfish, and often seen as a bad thing. Some would say a self indulgent person think about themselves a lot, they over eat, they care only about themselves, they take too much of a good thing, such as loads of cream cakes. These are the sort of things a person describes is the meaning of self indulgence.
But sometimes self indulgence can be a good thing. Take for example a person worn out from weeks and weeks of hard work at their company during the day, and at night when they go home from work, are building a new house for themselves & family. After all this hard slog as you can imagine, you'd be both very mentally and physically tired out. So if one day you said '' Sod it, I am going to be self indulgent today'', it would mean that you were not going to do any work at all, you were going to give yourself some pleasure like taking a trip to a Health Farm, have a sauna, have a swim, a lovely masage, a good meal, a drink of wine and totally chill out by yourself. You would then say you'd had a lovely self indulgent day.
Hope that explains the meaning well - mind you I just realised my example was written as a woman - though no doubt they could, I can't say I have ever known any woman that has literally come home from work and then set about laying bricks. I just got carried away with typing the answer.