People pursue threesomes for various reasons. First, the most common, are men who are looking to fulfill the fantasy of being with two women at the same time, especially if the women perform bisexual acts during the course of the threesome, otherwise known as "show time". ? There are also women who want to experience being with two men at the same time.

Also note that a threesome denotes open sexual contact between all members involved. If two people are having sex with a third but not each other, than it is not a proper threesome.

example: Two men doing the same woman at the same time (orally/vaginally or vaginally/anally) but with no direct man-on-man action is a 'gang-bang' not a threesome.

Bystanders that don't participate, or only masturbate do not count towards the toal numbers involved (its not a threesome if one person is the cameraman)

Likewise two or more couples engaging in sex in close proximity but not with each other is not a foursome (or sixsome, etc), but group sex.

And its not officially an orgy until you lose track of how many people are taking part.

Thanks for the information provided. It is very nicely explained by you.
Please provide more information on this matter.