In general, a petitioner is someone who submits a formal, written letter to an official entity – such as a court, government agency or political body – asking it to take a specific action.
In cases where such requests are made to courts, the petitioner is usually, but not always, someone who is dissatisfied with a lower court's decision, and wants another, higher court to review the matter.
When a lawsuit is submitted to a higher court for review, the petitioner can be the plaintiff or defendant who is unhappy with the outcome of the original case.
In a divorce, the petitioner is someone who initiates the legal process necessary to end a marriage. The petitioner does so by submitting specific paperwork, called a petition, to the appropriate court. In addition to ending the marriage, this paperwork is used to ask the court to deal with any issues.