Before sitting in the saddle you see some horse riders go in front of their horse and pull it forward why do they do this?

If you mean when they are leading their horse it is to make them move. Why do dog walkers pull their dogs forward? :) Sometimes a rider will move their horse forward after tightening a cinch to make sure the horse is not holding it's breath then will re-tighten the cinch before mounting to ensure the cinch is tight enough when riding to hold the saddle in place. Or they will move them to make sure that the cinch isn't pinching any skin, because if it is, it can rubs sores or bald spots under the girth.