Sexual selection is not the freshest of news. Darwin’s grandfather Erasmus had already commented on it. 
But a very pertinent question is why it occurs, or at least, what is selected. After all, why does a female finds a male sexy?
Two hypotheses could explain that. Fisher proposed the sexy gene hypothesis. He argues that, whatever the characteristic chosen by females, if it comes from a gene, that gene must become common within a population just because it has been picked up. A female that chooses a male with the sexy gene will have offsprings with that very gene, which in turn will be chosen by other females, spreading it.
The other hypothesis is the good genes one. According to it, when females prefer a certain trace, they are actually opting for a male’s good health, reflected on that given trace. For instance, a male with bright red feathers that uses carotene to increase the redness. Only a very healthy male has enough carotene to “waste” on plumage, so whoever gets the redder male will have healthier offspring and will have been favored by sexual selection.
Whatever the reason, good genes or sexy genes, the selected characteristics in the Birds of Paradise make them amazing. Scenes from BBC’s Planet Earth.
Both hypotheses seem to be correct. It all depends on the cost involved in the choice. When its not too cost-intensive for the females to choose (e.g. birds that gather for “exhibition parades” with heaps of males, sexy gene might prevail, like in peacock’s tails). In other scenarios, where choice uses resoures, be it looking around for males or exposing their presence to predators for the exhibition, the selected characteristic must have added value, a good gene.
But neither hypothesis explain how a characteristic begins to be selected. Why do females prefer a certain color, a song or any other thing? Where does the preference come from?
Like with most frogs, the song is used to attract partners. But in closer-related species, males don’t do the second part, they only chant the “win” bit. Now a bizarre fact.
When the P. pustulosus melody was played through loudspeakers to females of other close-related species, they like it better than their own species’ call! They prefered the screeching end, albeit they had never heard it before, since their own kind does not do it. Therefore, they already have the nervous circuit that make them like that kind of song better, but only the P. pustulosus males use them.
There is a bias preference amongst the females, who hear and prefer that frequency, but males of the other more than 40 species of the same genus can’t use it. 
Platy (left) and Green Swordtail (right). Same genus, but only one has a sword-shaped tail.
Other species follow the same path. In Xiphophorus fish, only the swordfish has its anal fin elongated. The longer the tail, more successful the owner. In close-related species, like platy, on which that long fin inexists, the same bias repeats itself. If artificial tails are attached to the males, thay become more popular. Again, females still prefer something they have never seen before. Probably because they prefer bigger males.
In more and more species, from birds with more intricate melodies to mite with specialized appendages on their pedipalps, we find characteristics in one species that are not present in others of the same genus, but are quite successful among them. It is about those who manage to explore a tendency already present.
The implication is that preference for a trait is inherent to females according to the more utilized senses. It could be the “eyes” on the pattern of a peacock’s tail, since they are vision-oriented birds and need to be in constant lookout for predators. And that crest is sure to attract attention. Senses and nervous circuits that are already in constant use for, say, searching food – like a spider’s sense of touch – are co-utilized or re-routed for sexual function. Which is expected, for our senses resources are limited. 
Nothing more fitting for evolution. Females preference is already there and males born with tiny variations. The one with a novelty-colored fin or a more refined song will be chosen and have more descendents rather than their rivals without those characteristics. With time, that gene becomes so ordinary as to level the success rate of all males, until one displays another interesting change, and the cycle starts over.
After all, the ladies like surprises.
 Smith, C. U. M. “Erasmus Darwin saw sexual selection before his grandson.” Nature 459, no. 7245 (Maio 21, 2009): 321. DOI:10.1038/459321d.
 Ryan, M., Fox, J., Wilczynski, W., & Rand, A. (1990). Sexual selection for sensory exploitation in the frog Physalaemus
pustulosus Nature, 343 (6253), 66-67 DOI: 10.1038/343066a0
 Ryan, M. (1998). Sexual Selection, Receiver Biases, and the Evolution of Sex Differences Science, 281 (5385), 1999-2003 DOI: 10.1126/science.281.5385.1999