The strength of your pet is randomly given to it after each level advancement. When a pet is born, it starts out as a (D) Class. As it levels up, it gets stronger and the bonuses that it gives out are provided to its master. For example, when a Tiger levels up from C to B, it will receive anywhere from 1 to 11 strength points. The bonus given depends on the pet type.
The "min/max" tells you the total bonus that a pet can have at that Rank.