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By definition, having lots of offspring = "success" or fitness in the natural-selection sense.

The male can easily make thousands of sperm. Since sperm are cheap/easy to make, males will maximize their fitness by trying to have as many matings with as many different females as possible. He goes for quantity of matings, not quality of mates.

However, the female is quite limited in how many eggs she can make, because each egg depletes her of a significant amount of resources. Mating with lots of different males will not necessarily increase the females's fitness, because one mating can provide her with all the sperm she needs to fertilize her eggs (however, there can be exceptions to this rule).

For the female, the best way to maximize her fitness is to make each egg count, by selecting the best possible father or fathers for her eggs. She goes for quality, not quantity.

Relative fertility as a function of number of mates, for two groups of Drosophila melanogaster (fruit flies). X-axis is number of mates, Y-axis is relative fertility. Solid lines are males, dashed lines are females. From Bateman, 1948.
With each additional mating, the male can father more and more offspring. But the fitness of the female maxes out at one mating.

Reference: Bateman, A. J. 1948. Intra-sexual selection in Drosophila. Heredity 2: 349-368.