Firmware is some software that is held on a chip actually inside
the device. The easiest of these to think of is BIOS flashing. Take, for instance, the situation with Abit KT7A boards. Some of the older ones will only be able to take the newer AMD XP chips if the bios is flashed to a newer version. The instructions in your guide are saying 'download and install the newer version of the software held on the chip (which is available from Steinberg) before going any further'.
A word of warning, though. Make sure you read EVERYTHING about the process of 'flashing' your Steinberg chips. I recently had the misfortune of attempting to flash my BIOS chip, only to find that the file I downloaded was somehow corrupt, and hence I knackered the BIOS.
I'm affraid these are very general notes because I don't actually have any of the above-mentioned devices. I would also check out www.linux-usb.org
to see what they say about your devices.