The nice folks at Google, obviously care about your account security and added an extra layer of protection, called Two Step Verification. I will not go into details about how it works, or how you can set it up, you can find all the answers you want here. What it does in short (for those of you lazy enough not to click the link) is that every time you want to sign in to your Google account (be that Gmail, Google Plus, or any other G service for that matter), except from your password, you also have to supply a pin number generated by an application you have installed on your phone. This extra step, minimizes the chance that someone else will gain access to your account. Neat huh?
One little problem I had, after I enabled Two Step Verification, was that I could not access the Android Market from my Phone. It kept asking me to sign into my Google account. Obviously, I was already signed in, since I was using the phone and there was no apparent way to tell the Market app to stop complaining. Turns out all you have to do, is go to Settings–> Applications –> Manage Applications –> All –> Market and then Clear Data. You will get a warning about data loss, but you can safely ignore it. That’s it. Market app will be working again.