It sounds like this character is painting. Most artists paint on a type of cloth called "canvas." "Taut" means "tightly stretched." Because canvas is cloth, normally it is flexible. If you stretch out the canvas and fasten it, it becomes firm, and not very flexible. Therefore, "taut canvas" is canvas cloth that has been stretched so that it is firm enough for an artist to paint on it.

taut: tightly drawn, tense, not slack. canvas: a heavy, coarse, closely woven fabric of cotton, hemp, or flax. taut canvas: a tightly woven piece of fabric.