Use the adjective monogamous to describe a person or animal who has only one mate. Beavers are one of only a few mammals that are truly monogamous, raising their young and living with a single mate.
There are many cultures in the world that aren't typically monogamous, meaning that men may have more than one wife or women more than one husband. However, most western, industrialized countries have made being monogamous the only culturally acceptable choice, and most American kids grow up imagining they'll marry one person and stay with that husband or wife until death. Monogamous comes from the Greek word monogamos, "marrying only once."