"Peter Please Answer" refers to the website "Peter Answers." This is a prank website with which one person can trick another at the same computer.
The quote comes from the site's use of "Peter, please answer the following question." The person typing must know the trick behind the website, which is that anything typed in the first field appears to be that phrase if a period is entered first. In reality, the person is entering the answer to the question in advance, before typing in the actual question in a separate field. Peter then appears to answer a question to which no one else should know the answer.