How to upgrade Mac Pro firmware?
Automatically Through Software Update

It is likely that OS X will automatically prompt you to download and install any recommended firmware update. This happens as part of OS X's software update process.

See About firmware updates for Intel-based Macs for the specific update steps on older Macs:


  Learn how to locate, download, and apply a firmware update to an Intel-based Mac computer.


All about the Mac Pro,1.1.

Manually via the Apple Support Site

Alternatively, you can find firmware updates on the Apple Support site. For example, this update appeared soon after the Mac Pro1.1 was released in 2006: Mac Pro SMC Firmware Update 1.1:


  The SMC Firmware Update adjusts fan behavior in the Mac Pro.


Download and run the updater. The updater will check and prompt you if it is required.

These firmware updates are effectively the same as a PC BIOS. As a Mac user, there is nothing to manage or update at the BIOS level; it is controlled by Apple.