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://bitcointalksearch.org/topic/m.813815 Is a post about another client, but it will cover many of your questions.
Topic: What is message signing? (Read 414 times)
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?
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