Let's get the hardest part out of the way. In US English it's pronounced "gwash": one syllable, just smash all the sounds together. Think "quash" but with a g, and a happier connotation.
What is gouache?
It's is a type of watercolor actually. It's made of the same stuff: ground up pigment particles and gum arabic (a syrupy base). The difference is that the pigment particles in gouache are much larger and there's more of them, which gives it its signature quality of bold opacity. It's flat too – unlike oils and acrylics, which also can be opaque but with a bit of gloss – gouache is totally matte. It dries of course, but the pigments sit on top of the paper (rather than nestling into the crevices like watercolor, or fusing together in plastic or oxidized oils like acrylic and oil, respectively). This means that if you get it wet again (or paint in wet layers) the previous layers will often pick right up and blend.