Sexual selection is a special subtype of Natural Selection, where the within-species competition here isn't so much for survival (as in natural selection) but more specifically for reproduction. Sexual selection is believed to be responsible for many differences between the sexes: male primates often (but not always!) have much larger bodies and canine teeth than females, traits that can be beneficial when competing with other males for access to female mates. And/or females may prefer larger-bodied or -canined males for whatever reason. In accord with the power of female preferences, sexual selection is invoked to explain why males of many species are so wildly colored or ornamented.
The plot to the right tracks growth in body mass (in kilograms) of male and female mandrills (Wickings and Dixson 1992: 132, fig. 1). The male is the top line and the females the bottom one. The arrows indicate timing of sexual maturity. Holy crap, by the time males are sexually mature, they are about 3 times the body mass of females.
The union of the ~25 lb female with the seemingly-paint-splattered, 75 lb male must be a truly terrifying sight.
Things I cited
Plavcan, J., & van Schaik, C. (1992). Intrasexual competition and canine dimorphism in anthropoid primates American Journal of Physical Anthropology, 87 (4), 461-477 DOI: 10.1002/ajpa.1330870407
Scott JE, Schrein CM, & Kelley J (2009). Beyond Gorilla and Pongo: alternative models for evaluating variation and sexual dimorphism in fossil hominoid samples. American journal of physical anthropology, 140 (2), 253-64 PMID: 19358294
Setchell, J. (2005). Do Female Mandrills Prefer Brightly Colored Males? International Journal of Primatology, 26 (4), 715-735 DOI: 10.1007/s10764-005-5305-7
Wickings, E., & Dixson, A. (1992). Development from birth to sexual maturity in a semi-free-ranging colony of mandrills (Mandrillus sphinx) in Gabon Reproduction, 95 (1), 129-138 DOI: 10.1530/jrf.0.0950129