A petition is a formal written request from one or more people to the Sovereign or Parliament. Petitions may be sent to Parliament and can be presented formally by an MP with a short speech or informally in the Petition Bag which hangs on the back of the Speaker's Chair. Petitions have a long history as members of the public have used them to make their feelings known about issues that concern them. A petition is often signed by several thousand people and Parliament receives over a thousand each year. Because the tradition of petitions is an ancient one, the rules about them can seem out of date. For example, up until very recently a petition had to be hand-written and begin with the words, "To the honourable, the Commons of the United Kingdom in Parliament assembled".
Further information on this subject can be found from the following links.
Rules on Public Petitions
Private Bills before Parliament