An open relationship means having more than one romantic or sexual partner at a time. Its an arrangement that both parties agree is non-exclusive or non-monogamous. As one or both partners engage in romantic or sexual activities outside the relationship, the arrangements agreement aspect is key.

What does it mean when he says he wants an open relationship?

An open relationship is distinctly different from cheating in that there is no secrecy, dishonesty, or subversion. By definition, an open relationship requires a consensual agreement by both partners to engage in relations with people outside the primary relationship.