It upgrades your remote to the newest version of it's software. Firmware is the name of the software that is embedded inside your remote.

It is generally a good idea with devices that can be upgraded (like computers, etc) to stay up to date with this stuff. Rule of thumb is if you are broken don't fix it. Generally wait about 2 weeks to make sure there aren't any problems before you upgrade.

In this case I would upgrade given all the issues with the Neo's (mine is actually going back today, my Pronto 1000 is on it's way becuase it won't learn the codes for my X10 lights).

If you're gonna use NeoEdit and custom configure your Neo then yes, do this upgrade. I did it 2 nights ago and it was fine. Haven't seen but 1 or 2 problems with it which is pretty good.