Unlocking on the Atrix means two different things.
SIM unlock: Doing this allows you to use SIMs from other carriers. If you have an AT&T Atrix for example you could use a T-Mobile SIM (although the Atrix only supports T-Mobile's Edge frequencies) or more importantly you could get a SIM in a different country and avoid paying insane international roaming fees.
Bootloader unlock: Doing this allows you to change the bootloader on the phone; to ClockworkMod Recovery for example. The main advantage of doing this is that you can install third party ROMs, but also allows you to back up the complete state of the phone on ROM form.
SIM unlocking is permanent but doesn't void your warranty and often times your carrier will give you the code to do it. Bootloader unlocking can never be undone, voids your warranty, and your phone will forever display the word 'Unlocked' at the top of the screen during the part of the boot that displays the Motorola logo.