The plaintiff argues that Texas should not base state redistricting on the distribution of its population, but rather on the distribution of its voters. The motivation for the case is to strip power from urban areas in favor of the rural conservatives.
Central to the conservative argument is that apportionment of representation by population size “dilutes” the power afforded to voters by distributing representation based on both the voting population and all the other people (kids, foreigners, prisoners, non-voters) who happen to live in a state House or Senate district.
In other words, the plaintiff believes that government representatives do not serve all the people in their district. The plaintiff believes that government representatives serve only the people who vote, and everyone else can suck eggs.
The potential impact of this case dwarfs the recent decisions upholding the Affordable Care Act and legalizing same-sex marriage. While those cases have sex-appeal to the general public, a case about apportionment of legislative seats must seem dull in contrast. But, if the Supreme Court bites on the argument that only voters should count for apportionment purposes, there will be a fundamental shift in political power that will make the Republicans current gerrymandering of their way into entrenched legislative power seem like weak tea indeed. There would be a massive shift of representation away from urban populations to rural areas and older white voters would exert an even more outsized influence on the body politic. This could cement extreme right-wing control of state and federal legislative bodies for another 40 or 50 years.