Concealing unfaithfulness with a beard Edit
In early usage of the term, the "beard" poses as the partner of a second person, while the second person is actually in a relationship with a third person, who is, in turn, married and cheating on his or her partner.
This scenario is a central premise of Woody Allen's 1984 film Broadway Danny Rose. The titular talent agent is the beard, pretending to date Tina's, a single girl who is having an affair with married singer Lou Canova. By posing as Tina's date, Danny can bring her to Lou's performances without drawing attention from Lou's suspicious wife. The term "beard" is a running gag used four times (e.g. "I'm only the beard") when Tina's relatives assume Danny is Tina's previously mysterious lover.
Concealing sexual orientation with a beard Edit
Another recognized usage applies to a person who serves to camouflage the sexual orientation of their companion, by being of the gender that conflicts with that orientation.
A media example is the episode "The Beard" of the television series Seinfeld, in which Elaine Benes acts as the beard accompanying a male homosexual friend, to suggest that they have a heterosexual relationship.
Many of the reported lavender marriages of 1920s Hollywood, and the reportedly similar 1955-'58 marriage of Rock Hudson, could be cited as involving such beards (though the word in this sense is said to have arisen only in the mid-1960s.) Taking seriously the claim of his wife, Phyllis Gates, that she was heterosexual (or assuming she may have had no real need to avoid being seen as lesbian), and in light of the danger that Hudson's homosexuality is accepted as having posed for his film career, it would be said that she was a beard for him, but not the reverse.