Monogamy is when you are married to, or in a sexual relationship with, one person at a time. Humans are one of the few species that practice monogamy. Well, sometimes.
You may have heard of something called polygamy, which is having more than one spouse at a time. The difference between monogamy and its antonym, polygamy, lies in the prefixes. In Greek, poly means "multiple," while mono means just the opposite: "single." Therefore, if you are committed to one romantic partner at a time, you are in a monogamous relationship.