lack of self-control: being ruled by a bodily appetite instead of having power over it
The word is built from a picture. It literally means "no power" or "no mastery," a person who cannot keep the reins on some appetite. Its exact opposite is self-control (ἐγκράτεια), the strength to hold appetite in check. So this word names not the appetite itself but the failure to govern it.
In the New Testament the same word points at different appetites depending on the scene. When Jesus condemns religious leaders (Matthew 23:25), it is greedy, unrestrained consumption, the appetite of someone who grabs and then gorges. When Paul counsels married couples (1 Corinthians 7:5), it is the pressure of sexual desire that makes a long stretch of abstinence risky. The core idea holds steady across both: an appetite that has slipped its leash.
Because English has no single everyday word for it, translators reach for different ones from place to place, "self-indulgence" in Matthew and "lack of self-control" in Paul. It sits near other words for giving in to appetite, such as open, shameless indulgence (ἀσέλγεια) and the craving itself (ἐπιθυμία), but it is narrower than either: it names the specific failure to master what ought to be under control.