The sexual fantasy, desire to expose one's partner, naked (in reality or through images), to another individual, or other parties, groups.
It is believed, this is some form of perverse desire, to allow others to derive sexual pleasure, from the viewing of their partner, in a state of nudity.
In some instances, this can further evolve into actuality, where a third party, or multiple other parties, are allowed to actually engage in sex with the shown partner.
This, then would be 'swinging'.
Candaulism was first coined by Kraft Von-Ebbing in 1886.
It was proposed by R Sandf that in fact, Candaulism' was a subtle, veiled form of homosexuality.
The notion was, that by showing the images of their partner, they would imagine themselves as that person, and enjoy the reactions from those seeing the images.