Open relationships are those where one is in a relationship with a particular person, but they allow either one partner or both of them to have sexual relationships with people other than their spouses.
These relationships include polyamorous relationships, polygamy, polyandry, etc. There are open relationships where couples consent that one or both of them can have other sexual relationships, and there are those in which there is no consent. These are relationships where things are not defined, and the two might not even be married or planning to marry.