Oocca, the sky beings
The Oocca are a peculiar race, living in a city that stays afloat in the sky through propellers. An adult Oocca stands as short as the leg of an average man, has a yellow-feathered chicken-like body and the head of a pale-skinned human, with bulging eyes lacking pupils. The Oocca as children are nothing but a human-like head with small, featherless wings instead of ears. How, when, and for how long the development of their adult body occurs is unknown.
Oocca can walk on some walls using their sharp talons and despite their chicken shaped bodies, they can fly very well, especially as children when that is their only way of getting around, but still not well enough to fly from the surface to their city. For this they would use specially designed cannons, a large quantity of which can be seen in their city but it seems only one was left in Hyrule when they stopped visiting it.
The Oocca are believed among scholars of Hyrule to have been even closer to the Gods than their chosen people, the Hylians. In fact, they are also said to have had some hand in the creation of the Hylians, presumably as a civilization more so than a race. We do know the ancient Hylians were distinctly more advanced than their descendants and neighbouring cultures and the reason for this is apparently that the Oocca enlightened them. Like the Picori/Minish, the Oocca have created powerful magical and technological artifacts and allowed the Hylians to use them. Both their magic and their technology is unmatched in Hyrule, but they seem to rely on technology more than any of the other races. The Dominion Rod was one of their greatest magical creations. It had the ability to temporarily animate some aptly devised statues found all over Hyrule, which is proof that the Oocca allowed the Hylians to benefit of their advanced knowledge to build important structures like the Temple of Time (in which the rod was kept) and Arbiter's Ground (which held the spinster, a device compatible with mechanisms in the Oocca's city). Certainly, all of this can explain why the Hylian crest is a bird.
But in particular, we know that it was the Sheikahs' duty of waiting for and relaying the messages of the Oocca to the royal family of Hyrule, and an obligation that they held true to long after the messages stopped coming, even going so far as to build shrines in their villages to revere them. Eventually, the Dominion Rod became an item to be carried only by the Messenger to the Heavens (together with a Sky Book written in the Oocca's language and kept by the Sheikah) when the royal family wished to contact the Oocca (presumably the rod was used to recover the cannon through which a Hylian could reach their city). Over time, it seems, contact was ended by both parties for reasons uncertain (it does appear though, that neither part ever grew reservations about receiving such messages, since the Sheikah kept waiting and Link was well received by the Oocca).
The city in the sky is no place for people who cannot fly or scale vertical surfaces, some of its floors collapse if something heavier than an Oocca steps on them, and some of the areas of the city have no floor at all. All of this however, may be because the city has apparently fallen in a state of disrepair over time, because doors and locales are actually more than large enough for humans to stand tall. Or it could be that the damage was caused by monsters that entered the city attracted by the fragment of Twilight Mirror it housed at one time. Interestingly, although very concerned, the Oocca did not show any intention to fight off these intruders, even though some of them were locked up in cages. It would seem they are an ostentably pacifist people.
What relationship, if any, the Oocca may have with Hyrule's other cloud-dwellers, the Wind Tribe, is unknown. The two have never been seen together. However, a relation between the two could explain the size of doors and locales in the City in the Sky, and we do know the Wind Tribe raised birds, some with magical abilities and training and both tribes had more advanced magic and technology (which the Wind Tribe supposedly received from the Minish). Perhaps the Occa were raised and trained by the Wind Tribe to mantain contact with the land dwellers? No one remains who can tell.