Open relationships are part of the larger category of consensually non-monogamous relationships. They are relationships in which both partners can pursue sex, and sometimes emotional attachments, with other people.
Open relationships differ from swinging, in which partners have sex with other people at parties and where the relationships are purely sexual. They also differ from polyamory, where partners can pursue more than one committed relationship at a time. Open relationships are sort of the middle ground between swinging and polyamory.
While swingers tend to keep their extramarital relationships to the realm of sex with other established couples, and polyamory is all about having multiple committed, romantic partners, people in open relationships can usually have sex with others they feel attracted to—with the caveat that these other relationships remain casual. In other words, you can have sex with whomever you want, but you can't fall in love with them.
One study discovered that about one in five adults had been in some form of an open relationship in their lifetime. Another survey found that 31 percent of women and 38 percent of men would prefer a non-monogamous relationship. In general, younger respondents were more likely to prefer non-monogamy than the older crowd.