A man and woman have a relationship and possibly live together. They are a couple but they have agreed that they can both have sex with other people.

and sure they both can have more then one relationship with others too

open relationship has no proper defination,we uses this like.... meeting someone and if you findes him/her suits to you then live togather(how long you want) and if anyone wants relation without any commitment is also like an open relationship..or you can say that spending some time(may be some days or one or two months for spending some good time including sex) is also like an open relationship

It means that you have a regular partner whom you connect with on an emotional and sexual level, but both people decide that it's ok to have sexual encounters with other people, outside the main relationship.