Yes, monos are brackish to marine water fishes. In the wild they swim in and out of rivers all their lives, and they do have quite a high tolerance for reduced salinity. But that said, while some people have kept them in freshwater permanently, this usually doesn't work, and the fish eventually get sick. At the very least, they become nervous and their colours go grey.
You don't need a high salinity to keep them happy, and anything from SG 1.005 at 25 C will do. Ideally, you'd keep them at around half-strength seawater, SG 1.008 to 1.012, but provided the water is hard, basic, and very clean, you have some leeway here. They do of course thrive in marine tanks, even reef tanks.
Maximum length under aquarium conditions tends to be around 15 cm, and they do need a big aquarium with ample swimming space. I'd find it hard to recommend them for a tank less than 210 litres (55 gal.). They are largely carnivorous, and as well as good quality flake and pellets, consume all sorts of wet-frozen invertebrates and seafood. Generally very easy to care for.
Social behaviour is odd. While generally assumed to be a schooling fish, under aquariums individuals (and sometimes pairs) can become remarkably territorial. Best kept in groups of three or more to avoid bullying, and from personal experience, mixing with some other, equally active tankmates (such as scats) does seem to help keep them good natured. You can keep a single specimen, but it is apt to be nervous, so choose tankmates with care.
There's more on my Brackish FAQ, and even more in my book, but this should be enough to be going along with.
Cheers, Neale
The other day I was at a fish store and saw the cutest little mono fish and I really want some of them now. And the dealer said it was a brackish fish but I just wanted to be sure about them, like what water conditions do they need, and how big of a tank, and all that stuff. So please let me know!!!