In traditional usage, a cuckold is a man whose wife has been having an extramarital affair. It only applied to men because it was bound-up with retrograde notions of male ownership of women. (In the 16th and 17th centuries, women in analogous situations were sometimes called "cuckqueans," but this word is considered archaic today.) To be made a cuckold was considered an extreme humiliation as it implied that you were such a weak loser that you could even protect you most intimate possession from "theft." (To call a man a cuckold is a traditional insult in Europe akin to the contemporary "f--- you." It even has it's own hand gesture.)
Modern fetish cuckolding is a form of BDSM role-play in which a committed couple eroticizes the conditioned fears and cultural baggage they have about gender roles, sexual fidelity, and emotional intimacy in the relationship. If the play moves beyond the couple's fantasy bedroom talk to involve people it may be considered a form of swinging or polyamory depending on your definitions of those things and the specifics of the outside relationships. But what distinguishes fetish cuckolding from other forms of multiple partner sex is that the man is deriving a sexual thrill from the emotional and/or psychological pain of the idea that his wife is having sex with another. If there isn't some sexual thrill related to feelings of shame about that; to the notion that he is deprived, cheated, failing, etc. It isn't cuckolding. (So, for instance, people truly committed emotionally to "free love" cannot be fetish cuckolded, as they do not feel any sense of jealousy, humiliation, or loss at the idea of their usual partner having sex with others.)
The key difference between fetish cuckolding and the traditional usage (which is still standard outside of the fetish and alternative lifestyle communities) is that the man (1) a knowing and willing/accepting accomplice in the arrangement, (2) getting sexual and/or psychological gratification from it. In traditional usage, a man who knew of and was at peace with his wife's continuing infidelity was called a "wittol" (From "wise," in the sense of knowing, cuckold.) That this word is not used in fetish cuckolding emphasizes its BDSM aspect; part of the fun is the idea of compulsion to her desires, or a better ("real") man, or your own base uncontrollable needs, etc. In another interesting modernization from traditional usage, the woman is described as having "cuckolded" her man, whereas traditionally the woman's new paramour would be described as the active party – "I've been cuckolded by Arthur the fishmonger" – the wife being regarded more as property. Although the cuckold prototypically (and usually) refers to a married couple where the wife has sex outside the marriage, the evolution of relationships in our time has led to its extension to non-married couples, same sex couples, and even to situations where the man is the polygamous partner. While any committed couple can play kinky psych games with trust and intimacy, however, only a situation of male submission unlocks the deep cultural baggage of the meaning of masculinity that is at the heart of the fetish.