So, what the artist is doing here is layering lots of transparent colors on top of one another to achieve the neutrals (the browns, grays, and blacks) in the painting. It's a common technique for watercolor, but you can achieve it with other media (this piece looks like it may have been done digitally, but I think the same principles still apply). In general, this technique is called glazing, but not all artists use such intense colors in their glazes.
The artist who comes to mind when I see this kind of painting is Peggy Macnamara. She's got a book that describes her process really well (Painting Wildlife in Watercolor) if you want to see it in action.