The common law definition is the voluntary union for life of one man and one woman to the exclusion of all others.
The Supreme Court of the United States in Loving v Virginia (388 US 1, 1834): "Marriage is one of the basic civil rights of man, fundamental to our very existence and survival."
And in Fearon v Treanor, New York Court of Appeal (1936) 272 NY 268:
"Marriage is considered a civil contract, but of a peculiar character and subject to peculiar principles.... It, certainly, does differ from ordinary common-law contracts, by reason of its subject-matter and of the supervision which the state exercises over the marriage relation, which the contract institutes.... While the marriage relation, in its legal aspect, has no peculiar sanctity, as a social institution, a due regard for its consequences and for the orderly constitution of society has caused it to be regulated by laws, in its conduct as in its dissolution.
"Marriage is more than a personal relation between a man and woman. It is a status founded on contract and established by law. It constitutes an institution involving the highest interests of society. It is regulated and controlled by law based upon principles of public policy affecting the welfare of the people of the state. Marriage, as creating the most important relation in life, as having more to do with the morals and civilization of a people than any other institution, has always been subject to the control of the legislature. That body prescribes the age at which parties may contract to marry, the procedure or form essential to constitute marriage, the duties and obligations it creates, its effects upon the property rights of both, present and prospective, and the acts which may constitute grounds for its dissolution.
"There are, in effect, three parties to every marriage, the man, the woman and the state.... Marriage is not a contract within the meaning of the provision of the Federal Constitution which prohibits the impairment by the States of the obligation of contracts.The Domestic Relations Law provides in great detail when and how marriage may be entered into, how the relation may be dissolved, the grounds for divorce and annulment, the rights and liabilities of husband and wife, the age at which the relation may be entered into and the class of persons who are disqualified from marrying.
"From time immemorial the state has exercised the fullest control over the marriage relation, justly believing that happy, successful marriages constitute the fundamental basis of the general welfare of the people. Our people believe that marriage should be entered into freely as a matter of choice, not through fear, restraint, or compulsion. The marriage state ought not to be lightly entered into. It involves the profoundest interests of human life, transmitting its complex influences direct to posterity, and invading the happiness of parents and near kindred."
In National Pride At Work v. Michigan (2007):
"In Michigan, marriage is recognized as inherently a unique relationship between a man and a woman. Marriage triggers legal rights, responsibilities, and benefits not afforded to unmarried persons, pursuant to a compact that is public and social in nature. Marriage is a civil contract, but it is not a pure private contract. It is affected with a public interest and by a public policy. The status of children, preservation of the home, private morality, public decency, and the like afford ample grounds for special treatment of marriage as a contract, by statute and decision. In recognition of its public and social nature, courts have cast about it the protecting mantle of presumptions, sustaining validity of marriage, said to be the strongest known to the law."
The US Code, at Title 1, Chapter 1, ¶7, defines marriage as:
"In determining the meaning of any Act of Congress, or of any ruling, regulation, or interpretation of the various administrative bureaus and agencies of the United States, the word “marriage” means only a legal union between one man and one woman as husband and wife, and the word “spouse” refers only to a person of the opposite sex who is a husband or a wife."
The law can and has been changed by some governments (eg. Canada) exercising their jurisdiction over this area of family law, to allow marriage between two persons of the same sex.
There has been much political debate on opening up the instutution of marriage to same sex couples, which now runs concurrent to the smaller but much older lobby by fundamantalist Mormons, amongst others, to legalize polygamy.