Petition
A petition is a formal written request submitted to a court or other governmental body asking for a specific action. In appellate practice, petitions are used to ask a higher court to review a lower court's decision, such as a petition for a writ of certiorari to the U.S. Supreme Court, which accepts only a small fraction of the thousands of petitions filed each year. Petitions also start some proceedings directly, such as bankruptcy.
A petition is a formal written request submitted to a court or other governmental body asking for a specific action. In appellate practice, petitions are used to ask a higher court to review a lower court’s decision, such as a petition for a writ of certiorari to the U.S. Supreme Court, which accepts only a small fraction of the thousands of petitions filed each year. Petitions also start some proceedings directly, such as bankruptcy.
Example: A party that loses in a U.S. Court of Appeals may file a petition for a writ of certiorari in the Supreme Court; out of the roughly 7,000 petitions filed in a typical year, the Court agrees to hear only about 100 to 150.
Common misconception: Filing a petition does not mean the case will be heard. In the Supreme Court, a denied petition ends the case there, and the lower court’s decision stands.
Sources: https://www.law.cornell.edu/wex/petition; https://www.law.cornell.edu/wex/writ_of_certiorari