A consensual open relationship is one in which both partners have agreed that one or both of them may be sexual with other people, without it being called cheating. If both parties haven't agreed, then it isn't consensual - it's cheating.
Open relationships are similar to polyamory, with some subtle differences. In open marriages/relationships, each partner may pursue or have other sexual partners, and doesn't necessarily need to share any specific details with their primary partner or spouse. In polyamory, a person may have more than one complete intimate relationship (romantic and/or sexual) happening simultaneously, and typically maintains open communication with each partner about it. If you are interested in or into polyamory, please check out my page on polyamory.
Successful open relationships can be complicated. If you and your partner are in an open relationship, or thinking of opening your partnership up to other sexual or romantic partners, it may be helpful to talk to someone about how to do it best. I can help.