What is Bigamy?

Legal Definition
In cultures that practice marital monogamy, bigamy is the act of entering into a marriage with one person while still legally married to another. Bigamy is a crime in most western countries, and when it occurs in this context often neither the first nor second spouse is aware of the other. In countries that have bigamy laws, consent from a prior spouse makes no difference to the legality of the second marriage, which is usually considered void.
-- Wikipedia
Legal Definition
The illegal act of marrying someone while lawfully married to another. The bigamous marriage is considered void when it was entered into and may be annulled.
Legal Definition
Crim. law, domestic relations. The wilful contracting of a second marriage when the contracting party knows that the first is still subsisting; or it is the state of a man who has two wives, or of a woman who has two husbands living at the same time. When the man has more than two wives, or the woman more than two husbands living at the same time, then the party is said to have committed polygamy, but the name of bigamy is more frequently given to this offence in legal proceedings. 1 Russ. on Cr. 187.

2. In England this crime is punishable by the stat. 1 Jac. 1, c. 11, which makes the offence felony but it exempts from punishment the party whose husband or wife shall continue to remain absent for seven years before the second marriage, without being heard from, and persons who shall have been legally divorced. The statutory provisions in the U. S. against bigamy or polygamy, are in general similar to, and copied from the statute of 1 Jac. 1, c. 11, excepting as to the punishment. The several exceptions to this statute are also nearly the same in the American statutes, but the punishment of the offence is different in many of the states. 2 Kent, Com. 69; vide Bac. Ab. h. t.; Com. Dig. Justices, ยง5; Merlin, Repert. mot Bigamie; Code, lib. 9, tit. 9, 1. 18; and lib. 5, tit. 5, 1. 2.

3. According to the canonists, bigamy is three-fold, viz.: (vera, interpretative, et similitudinaria,) real, interpretative and similitudinary. The first consisted in marrying two wives successively, (virgins they may be,) or in once marrying a widow; the second consisted, not in a repeated marriage, but in marrying (v. g. meretricem vel ab alio corruptam) a harlot; the third arose from two marriages indeed, but the one metaphorical or spiritual, the other carnal. This last was confined to persons initiated in sacred orders, or under the vow Of continence. Deferriere's Tract, Juris Canon. tit. xxi. See also Bac. Abr. h. t.; 6 Decret, 1. 12. Also Marriage.
-- Bouviers Law Dictionary
Legal Definition
The criminal offence of willfully and knowingly contracting a second marriage (or going through the form of a second marriage) while the first marriage, to the knowledge of the offender, is still subsisting and undissolved. Com. v. McNerny, 10 Phila. (Pat) 207; Gise v. Com., 81 Pa. 430; Scoggins v. State, 32 Ark. 213; Cannon v. U. S., 116 U. S. 55, 6 Sup. Ct 287, 29 In Ed. 561.

The state of a man who has two wives, or of a woman who has two husbands, living at the same time. The offence of having a plurality of wives at the same time is commonly denominated "polygamy;" but the name "bigamy" has been more frequently given to it in legal proceedings. 1 Russ. Crimes, 185.

The use of the word "bigamy" to describe this offence is well established by long usage, although often criticised as a corruption, or the true meaning of the word. Polygamy is suggested as the correct term, instead or bigamy, to designate the offence of having a plurality of wives or husbands at the same time, and has been adopted for that purpose in the Massachusetts statutes. But as the substance of the offence is marrying a second time, while having a lawful husband or wife living, without regard to the number of marriages that may have taken place, bigamy seems not an inappropriate term.

The objection to its use urged by Black-stone (4 Bl. Comm. 163) seems to be founded not so much upon considerations of the etymology of the word as upon the propriety of distinguishing the ecclesiastical offence termed "bigamy" in the canon law, and which is defined below. from the offence known as "bigamy" in the modern criminal law. The same distinction is carefully made by Lord Coke, (4 Inst. 88.) But, the ecclesiastical offence being now obsolete, this reason for substituting polygamy to denote the crime here defined ceases to have weight. Abbott. In the canon law, the term denoted the offence committed by an ecclesiastic who married two wives successively. It might be committed either by marrying a second wife after the death of a first or by marrying a widow.
-- Black's Law Dictionary
Legal Definition
Remarriage by one having a lawful spouse. See 20 Am. St. Rep. 377.
-- Ballentine's Law Dictionary