1) Self expression - coloring on a blank "canvas" (piece of paper), is a way for children and adults alike to express themselves. You can tell a lot about the way
a person is feeling by the images that they draw, the colors that they use, etc. It is important to give children a chance to express themselves, and not all children express themselves
through words and through writing, many use art.
2) Color recognition
3) Therapy - for many people (myself included) coloring is therapeutic. Regardless of whether it's scribbling, or coloring the "best picture ever", coloring can be a way to de-stress, after a busy morning of school work, wind down, and calm down, after the stresses of a day at school or work.
4) Grip/Control - many children learn how to hold a pencil, pen, marker, or colored pencil, by first learning how to hold a crayon. The small muscles needed for penmanship later begin to be developed while coloring.
6) Building motor skills
7) Focus - Paying attention to a single task for a length of time is necessary for coloring and for all sorts of things throughout one's life.
8) Boundaries - Another thing that children learn from coloring pages, with preprinted pictures on them, is how to accept boundaries. While a toddler or preschooler might scribble all over a coloring sheet, with no respect for the boundaries (lines on the coloring page), as the child gets older, they will begin to respect those lines, and make an effort to color between them. While I encourage blank paper coloring for free expression as often as possible, for many preschoolers pre-printed coloring pages are their first exposure to printed boundaries. This early exposure to boundaries in print, will be a huge help when handwriting time comes around, and the child has to respect the boundaries of the preprinted handwriting lines on the paper.
9) Milestone - This is the last little "importance" of coloring that I will mention for now, and that is that coloring in the lines is a milestone, a sense of accomplishment, the first step towards a successful academic career for many children. For many children coloring in the lines is just as important as counting to 10, counting to 100, reciting the alphabet, learning the multiplication facts, and so forth. It's a milestone that says "yes I can" do whatever I come across, and it provides children with pride, a sense of self worth, and helps them to feel accepted in a society that is often quick to judge, and slow to respond. This sense of accomplishment will carry them through life, and help them not to give up so easily, when something new comes along.