Being married to more than one person at the same time. Compare to polygamy which is not limited, by definition, to two husbands or two wives.
This is a criminal offence in most countries.
In Russell on Crimes (1826), the author points out that historically, and mostly based in canon law:
"... bigamy, in its proper signification, is said to mean only being twice married, and not having a plurality of wives at once".
But now it means being married to two persons at the same time (or, to use legalese, concurrently).
In Canada, the Criminal Code (2007) at ¶290 (extract only):
"Every one commits bigamy who in Canada, being married, goes through a form of marriage with another person....
"No person commits bigamy by going through a form of marriage if that person in good faith and on reasonable grounds believes that his spouse is dead; the spouse of that person has been continuously absent from him for seven years immediately preceding the time when he goes through the form of marriage, unless he knew that his spouse was alive at any time during those seven years; that person has been divorced from the bond of the first marriage; or the former marriage has been declared void by a court of competent jurisdiction."
In the United States of America, Scoggins v. State 32 Ark 205 (1877) the Supreme Court of Arkansas used these words:
Comedian Bob Hope is credited with this pun On the subject of bigamy:
"Two rites making a wrong."