Alimony, spousal support, and maintenance are all words for the same thing: one spouse paying support to the other after a divorce. It's designed to help a lower-earning spouse--or a spouse who's been out of the workforce entirely while raising children or taking care of the household--to get through the divorce process and transition into being self-supporting.
Over the last decade, alimony has become less popular with courts. The nationwide trend is to award support in fewer and fewer cases, and to keep the duration pretty short. In cases where the spouses are both employed and there isn't a large disparity in their incomes, it's unlikely any supportw would be awarded at all. The exception to the new rule is when the marriage lasted longer than ten years, in which case alimony is nearly automatic unless the spouses' earning capacities are the same.
Some states, like Texas, have laws limiting alimony payments to a certain period of time. In other places, alimony ends automatically when the spouse receiving it remarries or begins living with a partner. And in many cases, the termination date for alimony is included in the marital settlement agreement or judgment when the divorce proceedings are finalized.