Someone else may have a more informative answer but here is the short version (that I believe to be essentially correct):
Some people have constant problems with NICS checks because they are similar in name, DOB, etc. to someone who is prohibited. Or, they had a security check done by an obscure agency and each time they apply to NICS the NICS folks have to chase down someone at that agency to find out what the flag is from, i.e. innocuous security background check or investigation of a terror suspect.
If you want to avoid all of that, you can voluntarily give the FBI (I believe it's the FBI and not BATFE) a TON of information on yourself and they will thoroughly check you out. If you pass they will issue you a UID (Unique ID #) that you can then give whenever you do a NICS check. It shortcuts the normal process, all the NICS folks do then is check that your UID is in the system, in your name, and that no new activity has happened since it was issued. Much quicker, no delayed results, you just have to give up your privacy to get the convenience.
Futuristic