When cantering, horses can canter on a specific "lead." If on the left lead, the left foreleg appears to be in front of the right. The right lead is the reverse.
A flying change is when a horse changes its canter lead without breaking stride, normally seen when changing direction. It is very difficult for a horse to perform a flying change under a rider, and it is normally only seen in well trained and fit horses. They can easily lose their balance and have to break stride or, worse, end up on both leads at once, a situation called "cross firing" or "cantering disunited" - not very comfortable for either the horse or the rider.