You can check if the device is still jailbroken by trying to install one of the other packages available here.

Or trying to run the MobileRead-developed kindlets, i.e. KUAL or Collections Manager or suchlike.
OTA == Over The Air. Amazon will wirelessly send the updates to your Kindle.
(There is a way to stop that:
Kindle_Touch_Hacking#Blocking_Official_Updates)
EDIT: ninjaed.