I find myself talking about this topic at the day job a lot. There seems to be a lot of confusion about this medium. But it's easily explained.
Simply put, gouache—pronounced gwahsh—is opaque watercolor. It is watercolor with larger pigment particles and/or chalk added to increase opacity. I like to say: "It's like if acrylic & watercolor had a baby." And maybe that is the best explanation, if a bit of an over-simplification.
With watercolor you work light to dark, increasing washes of color or the density of your pigment as you progress through the painting. With gouache you work dark to light like you do with acrylic or oil.
I only tend to use gouache for highlights or coverups. When I want a nice, true white highlight for a shine on something like a lip or eye I use my Winsor & Newton Permanent White. I had the opportunity to pick the brain of a local artist who works primarily (maybe exclusively?) in gouache before I made the choice between Zinc & Permanent White. He said he likes the highly matte finish of the zinc white, so I opted for the permanent white, which is a hint glossier and much more opaque. (I tried looking him up to link his work here, which is complex, highly detailed, & beautiful, but I can't seem to find his website anymore. I'll keep trying, though!)
The matte quality of gouache can be a very nice texture if that's what you're looking for in your work. It does add a sort of richness in the pieces I have seen. It also tends to reproduce digitally quite nicely.
I'm not going to regurgitate what's already been explained by artists more talented & knowledgeable than I, so instead I will direct you to some wonderful blog posts that explore the topic more in-depth:
Watercolor vs. Gouache by Felt Magnet
Winsor & Newton Gouache Tips & Techniques
Gouache: How White is that White? (Zinc vs. Perm White) by Dick Blick