The main improvements for Facebook 3.1.3 is the ability to watch videos, writing on event walls, and a change in how wide uploaded photos can be (now 720 pixels wide).
You can update to Facebook version 3.1.3 by hitting the App Store icon on your iPhone or iPod touch, or by using iTunes on your Mac or Windows PC.
iPad owners: the iPhone/iPod touch application will work on your device in low res mode. While you can scale it up to 2x mode, in my opinion, the text looks terrible. I still recommend that you use Safari to browse to the full Facebook website.