What is message signing?

[Geez]

This is super noob question: What exactly is "sign message" in BitcoinQt? I don't get it. Are the messages shown when I make a transaction? And how can you proof with them that you own your address? And how can phishing attacks trick me into signing my identity over to them?

[Blue88]

This is a fairly common question on the forums, using the forum search (or even just a carefully done Google query) may help you get answers quicker in the future:

https://bitcointalk.org/index.php?topic=70911.msg813815#msg813815  Is a post about another client, but it will cover many of your questions.