A marriage in which each partner is free to enter into extraneous sexual relationships without guilt or jealousy from the other WordNet 3.0 & Open English WordNet

Open marriage is a form of non-monogamy in which the partners of a dyadic marriage agree that each may engage in extramarital sexual or romantic relationships, without this being regarded by them as infidelity, and consider or establish an open relationship despite the implied monogamy of marriage. Wikipedia

A marital relationship in which each partner agrees that the other partner may have sexual relations with other people as he or she sees fit. Wiktionary

Type of marital relationship. Wiktionary (translation)