what does it mean to file a written answer to the petition of petitioner?

A "written answer" is any writing that identifies the court, the case number and the parties and that "answers" the divorce petition. A written answer can be as simple as a letter addressed to the court, with a copy sent to the petitioner's attorney. Most answers are what we call general denials, meaning the respondent (you) generally deny what the petition says, even if some of the factual allegations are true. When you send your answer to the clerk identified on the citation, send a copy and self-addressed stamped envelope and ask the clerk to file-stamp the copy and return it in the envelope.

If children or anything that you value is involved, you should at least consult a competent attorney for advice on how to proceed. Prefereably, you should employ the attorney to represent you.