Is there such a thing as an open relationship?
Yes -- if both people agree that it's fine for each person to
see/have sex with other people. It takes a lot of maturity and open
mindedness to have that kind of relationship.
Some supposed "open relationships" are one sided--one of the
people trying to get the other to accept them having affairs or
indulging in threesomes. Basically, if you don't feel comfortable
with the idea, tell then no.
An open relationship, as opposed to a monogamous relationship,
simply means that one or both of the partners are not required to
be sexually exclusive to the other. The exact nature of the rules
regarding outside sexual partners varies from couple to couple.