Most of you will probably be aware of the existence in many species of sexual dimorphism, when males and females of the same species are significantly (and consistently) different in appearance. Indeed, considering that we ourselves as humans belong to one of the species showing sexual dimorphism, then if you're not aware of its existence you probably need your parents to explain some things to you. However, in some species sexual variation doesn't just stop there. Allow me to present you with the concept of male dimorphism.
Most researchers would agree that sexual selection is a major factor in the differences between sexes. Sexual selection is often referred to as something separate from and often opposed to natural selection, but as with so many popular distinctions the difference is somewhat artificial. Basically, sexual selection makes the fairly obvious point that if a certain form of male is more favoured in reproduction, then it will tend to become predominant in the population. This may lead to divergence between the sexes because males and females may be under different selective pressures. For instance, male deer grow large antlers that they use in fighting each other for access to females. The females themselves do not conduct such fights, so for them all that headgear would be little more than an annoyance, and they don't have them. Often features arising from sexual selection appear downright disadvantageous for the individuals possessing them - bright colours or loud calls in a bird may attract more females, but they also attract more predators. It has been suggested that this may not be entirely a coincidence - because sexually selected features usually act as a proxy for indicating the reproductive fitness of an individual, then development of such inconvenient characters indicates the male has fitness to spare.
Nevertheless, it is exactly this conflict between selective pressures that is thought to underly male dimorphism. In the majority of known cases, the two forms of male that are present in the population are one in which the sexually selected features are well-developed (large size, ornamentation, etc.) while the other form is less accentuated and more similar to the female.
The best-known example of male dimorphism occurs in Atlantic salmon where the population contains both large males and smaller "jacks". Salmon live most of their lives in the sea and travel back into fresh water to breed. When they reach their breeding grounds, the large males will occupy a territory and start gathering a harem of females that they defend from rival males. Jacks, on the other hand, do not defend a territory. Instead, they wander around the breeding grounds trying to find females that are not being well-defended by a large male. When the guarding male is distracted, the opportunistic jack will rush in and attempt to mate with his females while his back is turned. Males intermediate in size between large males and jacks are absent, and would probably be strongly selected against, being too small to effectively defend a harem and too large to mate in secret. One might also wonder why the two forms persist in the population rather than one entirely displacing the other - I suspect that this may be because the selective advantage of each form actually increases proportionally to the percentage of the other form in the population. Sneak-mating jacks are more favoured in the presence of a large density of harem-guarding males, as the guards will keep each other's attention engaged. Harem-guarders have an advantage over jacks in having females readily on hand rather than having to seek out unguarded females, and would be advantaged if there were less other large males with which to compete.
Minor males may have other advantages over major forms. In some species of mite, major males develop thickened and sharply terminated third legs that are used in fights between males (which are almost invariably fatal for the loser). Minor males lack these spines, and so are unable to compete directly with majors. However, minor males live for longer than majors, probably because they have not invested as much energy into developing the secondary sexual features (Radwan & Bogacz, 2000). Similarly, antlerless deer known as 'hummels' occur at low frequencies within the population and have a reputation for greater overall health than their antlered counterparts. Auld (1887) relayed the comments of a Lord Lovat on the subject:
Sometimes stags have no horns. These are called humle stags. If naturally so, and otherwise perfect, they will thrash any other stags of their own, or even considerably greater weight. We have known several of them undisputed masters of their own herds.
Auld, R. C. 1887. Hornless ruminants. The American Naturalist 21 (8): 730-746.
Radwan, J., & I. Bogacz. 2000. Comparison of life-history traits of the two male morphs of the bulb mite, Rhizoglyphus robini. Experimental and Applied Acarology 24: 115-121.