I see this mentioned frequently. What is it used for? Do you use it to clean your brushes only?

Is there any particular brand to use?

It can be used for mineral spirits based paints.  It can be used to thin some paints such as Rustoleum, although acetone can be better.  

Mineral spirits is a great cleaner for many glues before they set, such as contact cement and floor glues.  

It is a component of Ed's Red gun cleaner, google up the mix.

I also use it to remove lanolin based case lube from my brass, and to clean the flame proof vent hood over my oven.  I have used it to clean heavy grease residue off car parts because it is safer than many solvents.

I use mineral spirits for cleaning many things. I last used it to prepare a stock for refinishing after stripping all of the old finish. Cleaned it good with mineral spirits after using steel wool to smooth the surface. Let it dry. Then 7 coats of hand rubbed tung oil.

If you are going to touch up a blued finish on a gun, clean it with mineral spirits first.

Its a good solvent and can be considered a 'dry-cleaning solvent' because it cleans without water and then evaporates. But it doesn't evaporate as fast as the better dry-cleaning solvents, like Naptha. For this reason its better suited for larger jobs involving washing with solvent, like greasy vehicle parts. Naptha, on the other hand, is better gun cleaner because it evaporates very quickly, leaving a clean, dry surface for lubricants.

The only thing I've used mineral spirits for is rattle can paint prep.  I no longer use it for that.  I've switched to Acetone for paint prepping.

You can mix it 50/50 with alcohol and it's a fast drying gun cleaner. It's pretty similar to kerosene but dries a lot faster. It works well for just tossing parts in a jar and soaking overnight. I do this at the shop sometimes when I don't have time to work on something so it'll be easier to deal with in the morning.

Hoppes #9 (orange container) is about 45% kerosene, 45% alcohol, 5% ammonia (a tiny bit of copper removing action), and 5% banana oil (for the smell).

I use it as a general purpose gun cleaner.  I'll strip down my shotguns and throw all the bits into a jar and let them soak overnight.  

I don't use it as a bore cleaner, but as a general parts cleaner it works fine.  I keep a large wide mouth jar full in my gun room, I can fit the receiver of my over/under shotguns in it.

Is it good to use for cleaning your brushes after they become filthy from cleaning your gun?

Unless I am inspecting a part or replacing a part (rebarrel, etc.), I just clean with CLP and microfiber. CLP = any firearm lube of your choice. NO need to be emotional. Pat Rogers proved these things can run on literally piss, in a limited capacity anyway.
Suppressors are another thing. There are tight bearing surfaces that for best RTZ performance, SHOULD remain free of build-up. For this, I use a CLR soak and a USGI brass/bronze brush. My cans stay sexy clean. I made the mistake of not cleaning a can once, and now it's about 4oz heavier than it started life, after about 5000 rounds of .223/5.56, and while it does RTZ consistently, the build-up in the back section does bother me as it's rather pronounced, and it fits very tightly on the muzzle device.

I just blast mine with brake cleaner or Gun Scrubber. But yes, it would be good for that too.

I use it on new parts when I purchase a new firearm to remove preservatives, etc. For example, on 1911s, I completely disassemble, pour some spirits in a plastic paint roller pan and submerge those parts. Use plastic brushes on the parts along with pipe cleaners. Do the same to frames and slides. As a matter of fact, Rock Island (Armscor) recommends mineral spirits on their 1911s for their initial cleaning. I did it with all my new 1911s to include my Dan Wesson, Colt, etc. I did it with hesitation on a highly polished blue 1911. Called the manufacturer first. No problem with the finish. Cleans great though on some dull / matte finishes like park'd it can leave a whitish residue. A wipe down with oil removes it very quickly and easily.

Same here. I spray the brushes with brake cleaner. The non-chlorinated brake cleaner is my go to gun cleaner.

Tried soaking a BCG several time for three day to remove carbon. Guess what, it didn't work. Carbon was still hard to remove.