As of my knowledge parametric design means a design which is built up on a formulatic structure having a limited inputs i.e., in case of gears we will have a base diameter, tooth thickness, tooth depth etc., and by using these data and calculate the addendum, deddendum etc, and finally building up the gear.
The main advantage in the parametric design is even if you change the given input data the design will automatically change accordingly to the data as it is built up on that.
This methodology is almost applied in every commercial and standardized design according to my knowledge.