1. To make a formal request via an organized group, and especially in writing, for something to be granted or changed. We've been petitioning for better healthcare laws for the last 15 years. The worker's union petitioned for farer wages and better working hours for all employees of the company.

2. To address a formal request to some person or body of authority for something to be granted or changed. In this usage, a noun or pronoun is used between "petition" and "for." Students from around the country have begun petitioning the government for free public education. You can petition your case worker for an extension on your deadline if you need one.