When it comes to federal agency action, it's useful to remember that agencies get their power from laws.
The Environmental Protection Agency, for example, was not created in the Constitution. Congress created the EPA through a law. Several laws set the boundaries of EPA authority. The one relevant in this case is the Clean Water Act. It also defines how people or entities can challenge EPA action.
In this case, a bunch of groups challenged an EPA rule defining "waters of the United States." The cases were directed into one appeals court, the Sixth Circuit. Usually cases start in the lower district courts, but the Clean Water Act contains a provision that certain lawsuits challenging EPA actions should go directly to appeals courts.
Many of the groups challenging the EPA do not want to be in appeals court, so they are challenging the authority of the Sixth Circuit. They say that the EPA action they are challenging does not qualify under the Clean Water Act as a type of action that should go directly to an appeals court.
For more background on the case (including why the challengers might prefer the district courts), see this SCOTUSblog report.
This case is on appeal from the Sixth Circuit Court of Appeals. The Sixth Circuit ruled it has jurisdiction, and the appellants challenge that decision.
A previous version of this report listed the case argument as October 10, 2017, not October 11, 2017. It has been updated. The graphic has also been updated to fix a version in which the arguments were reversed.