Colored pencils, the medium I use, have techniques unique to them. With any art media, however, the importance of color is universal.
When you view art, the difference between a flat-looking piece or one that has a richness to the eye is proportional to detail in hue. As we observe a subject, what may seem simple in color has depths that reveal they are not simple at all. Red is never just red, green is never just green, for example. Each color has many shades, varied hues within, and reflections of color from the environment around. There are sometimes unexpected colors within what your eye may see to be one overall color. The building blocks of what will portray specific colors may embody different hues combined. By capturing all this detail, we bring depth to an art piece. Art does not always require attention to minutia to accomplish this, many artist styles can show vibrancy in a few strokes.
An example of color depth is in "Petals and Folds", above. The mind says "yellow roses", but if you look at the piece, you do not see plain yellow in the entire work.