Dyed means coloured by soaking in a liquid. The colour goes right through rather than sitting on the surface.
Cloth, hair and wool are the usual things dyed, and dyed hair is the commonest use of the word by far. Painting sits on top; dyeing goes in. The spelling is worth noting, since the verb dye keeps its e in dyeing to keep it apart from dying. English has one vivid phrase in dyed-in-the-wool, meaning thoroughly committed to a view, from the practice of dyeing wool before it was spun.
1adjectivedyedColoured by being soaked in a colouring liquid.
“She had dyed her hair a startling red.”