Modernly, this is a term in the area of human sexuality describing a person whom a stable sexual couple (quite often husband and wife) allow into their relationship as a third sex partner. Naturally it is quite possible that this person will be a partner in other activities as well, but it is the inclusion in the sexual aspects of the relationship which makes a third a "third," and not simply a "very close friend whom the couple spends a lot of time with."

The general rule is, as an understanding, that the original couple will have had, and will continue to have, a stronger and more intimate bond between them than the new person they allow into the relationship. But the third does become part of a relationship itself for so long as all parties wish it to continue; the third is not a fling or a prostitute (even though some people will speak casually of finding "a third" for a one-time threesome). The dynamics of relationships are already highly complex so there are many, many possible aspects that such a relationship can take upon itself.

* The couple could be sexually committed, and expect the third to be sexually committed to this relationship as well, and not have sex outside the relationship.
* The couple could be sexually committed, but not have such an expectation for the third, who may be sexually involved with others outside the relationship (but be careful).
* The couple could be sexually open, with any of the three participants able to have sex with others outside the relationship, without upsetting the relationship (but be super-careful).
* The couple, having added a third into their relationship, could expect to only have sex when all three are participating; or to have sex as a couple and occasionally involve the third; or to have sexual encounters wherein either member of the couple may pair off only with the third from time to time.

But note that where a couple decides to bring in an additional sex partner for only one member of the couple, they are not bringing in a third. If a wife allows her husband to bring a mistress (or in some cultures second wife) into the house, or if a husband allows his wife to bring a male lover into the house, but this new person does not engage in sexual relations with both of the original couple, then they are simply a sexual adjunct for one partner, not a third in the relationship. For some couples, a third is sought specifically where health or other circumstances make it physically difficult for one partner to satisfy the sexual needs of the other.

The variety of human sexuality raises interesting dynamics for a third. In heterosexual couples, the third may, naturally, be of any gender. If one or the other members of the couple is bisexual, and the third is bisexual, then they may end up having any combination of sexual activities. A straight male with a straight female wife might still bring in a third who engages in threesomes where the sexual activity is uniformly heterosexual (with the male alternating between or simultaneously pleasuring the female participants, whose interaction with each other is limited to perhaps teasing banter); the same can happen in a relationship with two straight males and a straight female. In gay and lesbian couples, a third would most typically be a person of the same gender. But it is not impossible that a stable female couple of two bisexual women might bring a male third into their relationship, or that a stable male couple of two bisexual men might bring a female third into their relationship.

Finding a third is much like finding a stable sex partner in the first instance, though naturally the effort is complicated by the much smaller pool of people who are interested in becoming a third partner to an existing relationship. Some people try it as an adventure and discover they enjoy it, especially when the relationship role provides the opportunity to be the focus of receiving sexual attentions from two other people. It is noted to be much easier for gay couples to find a gay third than for heterosexual couples to find a bisexual third interested in having sexual relations with both the male and female partners of the original couple. In fact, in some circles a bisexual woman interested in becoming a third to an opposite-gender couple already including a straight man and another bisexual woman is called a "unicorn" in reference to the supposed rareness of such a person.

In some instances, a third comes into a relationship where one partner in the relationship has a former lover who wishes to become a lover to that partner again, and is willing to become a lover to the other partner as well (this was the case in my relationship; the return of my former sex partner as a third was eased by her being my cousin, and so not somebody who my newer partner saw as a threat to our established intimacy). In very rare instances, a three-partner relationship coalesces when one partner is nonmonogamously involved with two other people at the same time, and these two others find themselves willing to be intimate with one another. But in those instances, it is not necessarily apparent that one partner is a "third" relative to the other two.

For more info on this, here is sex columnist Dan Savage advising you on "Finding that perfect third for that threesome," and here is an awesome Reddit post on "How to open your marriage to a third." Blessings!!