A cuckold is a married man whose wife openly has sex with other men. In current usage it sometimes refers to non-married couples in committed relationships as well, although the traditional meaning is a man whose wife is adulterous. However, very often the cuckold is both aware and encourages his wife's "infidelity" and is sexually excited by it.
In plain English, a cuckold is a man who stands by and accepts his wife's infidelity, being sexually excited by her actions. He may have normal sexual relations with his wife part of the time, or he may accept that his wife has chosen another man to replace him completely in her sexual bed. As a consequence, many cuckolds end up raising children that aren't their own.