The judicial power is the power to finally resolve disputes: federal-question cases, suits between states, diversity cases, and the rest of Article III's list. A final judgment binds the parties, and the reasoning binds the future through precedent.
Read the clause itself, verbatim and in plain language, in the in-app Constitution.
The federal courts
District courts try cases (with juries where the Constitution requires); circuit courts review for legal error; the Supreme Court selects a few dozen questions a year by certiorariThe Supreme Court's discretionary review. Losing parties petition for a 'writ of cert'; four justices must agree to hear the case.Full definition in the glossary. Judgments are enforced by the executive and, for statutory interpretation, can be corrected by Congress simply passing a clarifying law, constitutional holdings are the ones only amendment or the Court itself can undo.
Constitution Annotated, Article III
Terms to know: jurisdictionA court's legal authority to hear a case: over the subject matter, the parties, and the territory.Full definition in the glossary · standingThe requirement that a plaintiff show a concrete, particularized injury, caused by the defendant, that a court can redress. No injury, no case.Full definition in the glossary · opinionA court's written explanation of its decision. The majority opinion sets precedent; concurrences agree with the result for different reasons; dissents disagree.Full definition in the glossary