A more thorough explanation:

United States v. Windsor is a Supreme Court case that ruled that the Defense of Marriage Act (DOMA) was unconstitutional. DOMA excluded same-sex married individuals from the definition of spouse, which violated the protections afforded by the Fifth Amendment.

For example, Edith Windsor and Thea Spyer married in Canada in 2007. After moving to New York City, and upon Spyer’s death in 2009, Windsor attempted to claim the estate tax exemption for surviving spouses. That claim was denied because under DOMA same-sex couples were not eligible to file for the exemption. Windsor paid the taxes but filed a lawsuit to reclaim that money and, therefore, challenge the constitutionality of DOMA’s key provision.

The Court found that DOMA’s definition of marriage sought to discriminatorily injure a class of persons. Even if a state legalizes same-sex marriage, DOMA’s applicability to 1,000 or more federal statutes and regulations would frustrate a state’s purpose in creating equality between homosexual and heterosexual couples. DOMA thereby creates tension between a same-sex couple’s rights under state law and federal law, resulting in a patchwork of laws that frustrates stability and predictability for homosexual couples.

Chief Justice Roberts filed a dissent in which he argued that the Court lacked jurisdiction to decide the case and also that DOMA was constitutional. Justice Scalia, in a dissent joined by Justice Thomas and Chief Justice Roberts, argued that Windsor redressed her injury in the lower court and no controversy existed because the Government supported her position. Justice Alito, in a dissent joined by Justice Thomas, agreed with the other dissents that the case before the Court lacked controversy and therefore was not properly before it.