The new software version is 6.2.2. Early reports are already in, and this update appears to add just one feature. Silk, Amazon's own web browser, now has full screen mode (like most Android web browsers).
This update is being pushed out over the air and you might already have it. If so, then you probably want to hack you tablet gain. That's easy; XDA Forum member and hacker Justin Case has already updated his BurritoRoot utility. It will work even after the latest update. You can find BurritoRoot 2 at the xda-developers forum (just not today; XDA went dark in protest of SOPA).
If you really want the update, you can download it direct from Amazon. Copy it to the kindleupdates folder. Then go into the settings menu and tell it to update.