I appreciate the info! I don't think I have access to that book (not sure if someone I game with has it). I have the SR4a and Street Magic that I purchased. I was playing a Mage in the group so wanted to have the info on hand. And haven't played in, uh, a long time.
Here I am hoping I'm not too late on this, but...
Restricted gear, the quality, has the purpose stated above. Namely to allow you one signature item/enhancement/what-have-you that exceeds the typical availability limit of 12. So. if your character's backstory involves some sort of super-soldier program, then you can express that in terms of qualities by giving that character the "Restricted Gear" quality (up to 3 times) and some high-end availability 20 cyberware, like r4 Muscle Toner, a Suprathyroid Gland, or Move-by-Wire 2. It's basically a quick way to bypass a step of character growth and development. Sam starts out with a prime-level piece of ware. Rigger starts out with a tank-buster Heavy Autocannon. Mage starts out with the kind of Focus that dragons go to war over. It can be abused like anything else, and it can be loads of fun too.
The R and F next to gear designates whether that gear needs a license to avoid police trouble (one assumes in UCAS territory. Laws are different from one block to the next with corporate extraterritoriality.) as is the case with Restricted gear, or whether you're going to draw special police attention on sight, as is the case with Forbidden gear.
So, Restricted gear is something which can be licensed like dynamite, a rifle, dangerous medications, certain tools and so forth. Forbidden gear includes things like military-grade weaponry, spy tools, poisons and insane drugs. Basically, restricted gear can be explained away with a tag on your SIN saying "he's a security contractor/bail bondsman/etc." whereas forbidden gear is going to take a lot of clever lies and supporting information to back up (or a fat bribe,) otherwise, it'll be bells and alarms for miles.
Both restricted and forbidden things can be purchased at character generation, provided that their availability rating is 12 or lower. The "Restricted Gear" quality allows one item of avail up to 20, subject to GM approval.