From the facebook widget?
If so then open facebook on the news feed screen - press where it says facebook, the screen with news feed/profile/friends/messages.... should come up, then hit the menu key. The menu will come up settings/refresh/About and Logout.
When I do that I get the following message: "Logging out will remove your FB data from this phone. Do you want to logout? I never logout because of that. But if I knew that my data wouldnt be removed/lost I would.
Ok, I tooked one for the team, I logged out of my Facebook account and then hit the FB icon again and I had to log in, after that everything I had before was there, I didn't notice anything being lost. So I do not know exactly what data they claim I lost.
When you logout of the facebook app on your phone it's the same as logging out on your personal PC. It removes your data so that it can not be accessed by another user. This means that someone else could log in to their FB account from your phone or computer and still not have access to your FB page and information. The FB app only acts as a portal to your account and once you log out your data will still be safe.