Once you have your tape hardware working, there shouldn't be a need to update the firmware or tape drivers. However you will often see this listed as a step to try in troubleshooting procedures.
Firmware is the software built in to your tape drive. This determines how the drive operates. Firmware is provided by the tape drive manufacturer. Some drive manufacturers have firmware upgrade tools built into a diagnostic suite. Eg HP provide HP StorageWorks Library and Tape Tools to help diagnose problems and upgrade firmware.
Drivers control how your operating system interacts with the tape drive. Drivers are typically supplied from three places: By Symantec; By the tape drive manufacturer; By the operating system manufacturer. Generally it is recommended that the Symantec driver is used. The latest Device Driver Installer for 10d can be found at http://support.veritas.com/docs/285593, and for 11d you need to know if you need 32-bit drivers or 64-bit drivers. If you are using a robotic library you also need a driver for the library itself. This is typically provided by the tape drive manufacturer or the operating system manufacturer.