In a lot of ways, children can learn the most, and gain the greatest skill at certain things while they are still very young. It might take an adult years to learn a new language, while children seem to take it up quite quickly. It is the same way with a number of physical activities. Children love to be moving and mimicking other people around them. Yoga is a great place to start an exercise regimen that will have lasting benefits down the road.
Yoga is a great place to start with children because they are naturally quite limber. Therefore some positions that you might find create an incredibly intense stretch, they will simply be able to fall right into place. Sometimes it seems as though they're made out of rubber bands, which really isn't very far from the truth. If you are very advanced at practicing yoga, you will not be able to teach all positions to children because they do not yet have the physical strength and agility for some of the poses. But if they are capable of getting into the pose with out any discomfort, it's not going to hurt them either.
It really seems a little strange to me at how we treat our children these days as though they were made out of paper machete. I remember growing up throwing rocks, jumping off of buildings, riding bicycles over huge ramps, and yet somehow I managed to survive with little more than a few bruises and scrapes. Comparing yoga to the types of reckless behavior I displayed as a child seems incredibly tiny by comparison. Therefore there is no real need to be incredibly careful about which positions you allow the child to attempt. If they can, and will, do the pose, it is just as safe and beneficial for them as it is for you. In many ways it's probably safer for them because there is less risk of injury.
There is an awful lot of hogwash circulating around out there that if children exercise too strenuously using weights or other things that it can be damaging to their bodies. Poppycock is all I have to say about that. No, you do not want your child learning to do free full stunt jumps from 10 story buildings, or trying to bench press 200 pounds. The simple fact is - they can't do those things anyway. They don't have the strength or agility. But swinging from the branches of a tree is not going to kill them (within certain normal limits of course). Children's bones are softer and their muscles far more flexible than adults. A fall or tumble that would seriously injure you will seem to have almost zero effect on a child. So it's perfectly fine for them to take those energies that might otherwise be used for swinging from trees and devote them to something that can give them some real benefit such as yoga.
So if you're looking for something to involve your child in some coordinated structured exercise, yoga is a fabulous choice. Many of the positions are also named after animals which makes it perfect for tying in a little storytelling while you exercise. Of course, it's going to help if you know how to do yoga as well and will give you a way to spend some quality time doing something constructive with your child that may very well become something that they carry with them all the way through their adult life.