At issue is whether spouses in same-sex marriages are entitled to the same employment benefits as those in heterosexual marriages.
In 2013, the city of Houston offered spousal benefits to employees in same-sex marriages just like it did for those in heterosexual marriages. A group of conservatives sued to block the move, essentially arguing that the US Supreme Court's decision legalizing same-sex marriage in the Obergefell case does not mean LGBT couples have equal rights.
In contrast, the city of Houston has consistently argued that the US Supreme Court's decision means all marriages are equal, so anything offered to heterosexual couples must be offered to same-sex couples, too.
The Texas Supreme Court originally declined to take the case on discretionary appeal after a lower court ruled in Houston's favor and against the conservative challengers. However, after pressure from Republican elected officials, including rabidly homophobic Governor Gregory Abbott, the state Supreme Court reversed itself and granted the appeal.
The conservatives who originally brought suit have repeatedly said they hope the case will eventually make its way to the US Supreme Court -- which has discretion whether or not to take the appeal -- and that any justices appointed by Donald Trump will help make a deciding majority to whittle away at same-sex marriage rights.