Coloring in a picture will command your child's full attention, as they concentrate on completing their work, and having the finished product show that they have done their best. This is a welcome assistance for parents who struggle to provide their children with experiences that will captivate their attention, only to find that their little minds and bodies start wandering after only a short time. So as a parent, you gain a short respite as your child works on their coloring page, your child gets to participate in a fun activity that teaches them as well. Which leads me to the next point.
As already mentioned free coloring pages are a great way to teach your child all sorts of things, numbers for example. There are different ways this can be done, one way would be to simply have the number somewhere on the page, such as the number 10, and then somewhere else on the page would be an object or animal cleverly twisted into that number. There could also simply be 10 of something on the page, you can get your child to color the page in and then count out how many apples for example there are, which will obviously correspond to the number on the page.