"marriage with more than one spouse," 1590s, from Late Latin polygamia, from Late Greek polygamia "polygamy," from polygamos "often married," from polys "many" (see poly-) + gamos "marriage" (see gamete). The word is not etymologically restricted to marriage of one man and multiple women (technically polygyny), but often used as if it were. Related: Polygamist; polygamize.
In Christian countries, when a man has more wives than one, or a woman more husbands than one, at the same time, he or she is punishable for polygamy ; but if there was a separate marriage with each the first marriage would be valid notwithstanding the subsequent ones, and the later ones would be void. The offense of contracting the subsequent marriage is now termed bigamy. But polygamy in the form of polygyny is allowed in some countries, especially among Mohammedans, and was held a matter of faith and duty by the Mormons. [Century Dictionary, 1895]