According to Article III, Section 2 of the constitution,
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;—to all Cases affecting Ambassadors, other public Ministers and Consuls;—to all Cases of admiralty and maritime Jurisdiction;—to Controversies to which the United States shall be a Party;—to Controversies between two or more States;—between a State and Citizens of another State;—between Citizens of different States;—between Citizens of the same State claiming Lands under Grants of different States, and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects.
This defines the jurisdiction of the federal judiciary. For example, the federal judiciary has jurisdiction to hear cases where a citizen alleges that their own state is violating one of their rights granted by the federal constitution and seeks injunctive relief, since that falls under "arising under this Constitution".
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction.
My understanding of "original jurisdiction" is that it basically means "you can file this kind of case in this court". And since this is in the constitution, Congress can't take it away.
However, as far as I can tell, it's not actually allowed for an American to sue their own state directly in the Supreme Court. They have to file in a federal district court and then appeal the decision if they don't like it. Legally speaking, why is that?