A more thorough explanation:

The Defense of Marriage Act (DOMA) was a federal law passed by the 104th United States Congress intended to define and protect the institution of marriage. DOMA specifically defined marriage as the union of one man and one woman, which allowed individual states to not recognize same-sex marriages that were performed and recognized under other states’ laws.

For example, if a same-sex couple got married in a state where it was legal, but then moved to a state where it was not legal, that state did not have to recognize their marriage. This meant that same-sex couples were denied many benefits and recognition that opposite-sex couples enjoyed, such as access to a spouse’s employment benefits, the recognition of the marriage itself, the rights of inheritance, joint tax returns and exemptions, and the right to cohabit together in a college or military housing.

DOMA also stated that "the word 'spouse' refers only to a person of the opposite sex who is a husband or a wife” and further states that “[i]n 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.”

One of the major provisions of this law was that a non-biological parent could not have a legal relationship with a child of the biological parent in a same-sex couple. Moreover, same-sex couples could not take medical leave to care for their partners or non-biological children. They also could not adopt children and during divorce proceedings, they could not petition the court for custody, visitation rights, or child support.

The supporters of DOMA believed that opposite-sex marriage was the only appropriate method for family formation and procreation. One of the major arguments from proponents of DOMA was that same-sex marriage could lead to alternative family formations and could even result in incestuous relationships and polygamous marriage. On the other hand, the opponents of DOMA claimed that DOMA’s definition of marriage as only between one man and one woman and other arguments were discriminatory on the basis of sex, and equated homosexuality with incest and polygamy.

In 2013 in United States v. Windsor, the U.S. Supreme Court struck down DOMA’s definition of marriage as only between one man and one woman. Furthermore, in 2015 in Obergefell v. Hodges, the Supreme Court struck down the section of DOMA that allowed individual states to not recognize same-sex marriages performed in other states. This result granted same-sex couples the constitutional right to marry.

It is important to note that in 2022, the Supreme Court decision in Dobbs v. Jackson opened up the possibility for the Court to reexamine its ruling in Obergefell in the future.