Regulators help manage the air that is used for each shot. For example, if the regulator is set at 130 BAR, the output pressure flows from the regulator at 130 BAR every time you pull the trigger. Having consistent pressure provides more accurate shot strings.
As you can see in the above example shot string, the airgun equipped with the regulator has a smaller deviation in pressure between shots than the airgun without the regulator. Thus, having a regulator provides a more consistent shot string than an unregulated model, but this is usually at the sacrifice of power and velocity.