When they refuse to hear a case it's the equivilent of placing the court's seal of approval on the lower court's decision.
A common misconception.
This is from Techlawjournal.com:
“Someone who is dissatisfied with the ruling of the Court of Appeals can request the U.S. Supreme Court to review the decision of the Court of Appeals. This request is named a Petition for Writ of Certiorari. The Supreme Court can refuse to take the case. In fact, the Court receives thousands of “Cert Petitions” per year, and denies all but about one hundred. If the Court accepts the case, it grants a Writ of Certiorari.
“Review on writ of certiorari is not a matter of right, but a judicial discretion. A petition for writ of certiorari will be granted only for compelling reasons.” Rule 10, Rules of the U.S. Supreme Court.
The U.S. Supreme Court’s certiorari process is covered in Rules 10-16, Rules of the U.S. Supreme Court.
The effect of denial of certiorari by the U.S. Supreme Court is often debated. The decision of the Court of Appeals is unaffected. However, the decision does not necessarily reflect agreement with the decision of the lower court.”