phpBB3 is the next version up. You're using it right now! It has a lot of new features
not present in standard phpBB2.
Your admin panel says you're up to date because your phpBB2 version is just that.
phpBB3 is a new package entirely. It's currently at the RC5 stage. You can use it on a live environment but you should be aware that you might have to make updates before it goes gold and you might find the odd bug in it. It also includes a converter which will move your users and posts but not your MODs (except the attachment and birthday MODs) or templates.