Monogamy is a marital practice in which a person is limited to a single spouse at any one time. The practice of restricting contact to a single spouse for a limited period of time, then ending that relationship before beginning another (though in practice there may be a brief overlapping time-period) is refered to a "serial monogamy."
Historically, monogamy was much less popular than polygamy (specifically polygyny) Mostly because of European expansion, monogamy is more popular than it was ever before. See article about Polygamy for details.
Note that the term "monogamy" is also used to mean confining a sexual relationship to one other person even in the absence of a legal status of marriage (for example, an unmarried heterosexual couple or a homosexual couple in a jurisdiction that does not recognize marriage between homosexual persons.) Monogamy in this sense is recommended by health professionals discussing safer sex practices.
Note also that unlike some other species, Homo sapiens is not "automatically" monogamous, and the existence of a legally monogamous relationship (marriage) is no guarantee of a monogamous one in fact. Some societies have formally or semiformally recognized that married persons may have other sexual partners outside of the marriage relationship, while in societies that do not condone this practice it is nevertheless not unusual.
Monogamy is occasionally used to mean having only one sexual partner during an entire lifetime.