When mates are determined by members of the same sex (usually males) competing for a mate, ornamentation distinguishes the sexes. For example, larger antlers become more attractive. The antlers are not really for fighting, at least not fighting to the death. If species really had death-matches, there would be very few viable mates next season. Aside from drawing attention to oneself, ornaments, especially those that are detrimental to their bearer, are signs that the possible mate can survive with such handicaps. These ornaments also take extra energy to grow and support. The greater the ornament, the more fit its possessor must be to survive.
The Sexy Son Hypothesis (I'm not making this up!) is based on the idea that a female will seek in her mate the best genes for her own son. If her son is well endowed, he will be more likely to reproduce and pass along his genes. Essentially, sex appeal becomes its own reason to exist. This is essentially the much-abused "selfish gene."
There is some relationship between the amount of dimorphism and the number of sexual partners in species. However, while these are fun to consider and wonder about, there is not enough to say that one causes the other, or that they are even positively correlated. However, if you are an evolutionary biologist focuses in dimorphism, please get back to the lab and get me some answers!
When thinking about evolution, most people remember natural selection, but sexual selection is just as important, especially when an animal looks weird, like the hairless ape.