As it pertains to people and dating, the term exclusive is an adjective which describes a couple and their relationship with one another. Couples often become exclusive in time, once two people mutually agree that they are serious about romantically pursuing one another.
As the word exclusive literally means limited to a single individual or group, exclusive couples are typically monogamous. However, as a wider spectrum of relationships have grown to become accepted, some people may define exclusive in a different way. For example, a non-monogamous person may have an exclusive relationship with one person they date and have romantic feelings for, but still have sex with other people.