According to the Encyclopedia of Arda, the Kine of Araw were descended from the even greater kine (cattle) of Orome the Hunter, who was known to be the master of beasts and birds. As Orome was chosen to lead the Elves on the Great Journey, he might have intentionally (or accidentally) left his livestock in the East.
They presumably lived in the areas immediately adjacent to the Sea of Helcar, relocating to their present location around the Sea of Rhun when that great ocean dried up.
Vorondil the Steward of Gondor ventured to the Far East and hunted one such beast, utilizing its great horns to craft the exquisite Horn of Gondor. For the lengthy years afterward, it became an heirloom of Gondor's stewards, handing it down to their oldest son for innumerable generations.
However, its doom drew ever nearer, just as Sauron’s shadow returned from the depths of the East. During the War of the Ring it was carried by Boromir, son of Denethor. It was only when Boromir was assailed by hundreds of Uruk-hai, that the horn was eventually broken. The Uruk scimitars and broadswords clove the great horn in two, rendering it useless. After being presented to his grieving (and insane) father, it was buried with him.
According to Appendix A of the Lord of the Rings, the Kine of Araw were far larger and splendid than common, earthly cattle (like Old Bessie). Their hides were a gleaming pallid white that reflected the sun rising from the Gates of Morning in the East.
The horns attached to their gargantuan bodies were colossal in size, giving the kine an air of grandeur. While nobody knows what the kine really looked like, their size and scant description that we possess may give them an appearance similar to the real-life Texas Longhorn.
There are certain parallels between the Kine and the real-world Aurochs. The Aurochs is considered to be the ancestor of modern cattle; they were large, dangerous animals with great horns living across North Africa, Europe, and most of Asia. The Aurochs was driven to extinction in the 1600s by heavy hunting, especially by royal families across Europe.
Kine is a rather archaic English word, meaning "cattle." As Tolkien was deeply fluent in Old English, Welsh, and Scottish, he would have used the term rather than a more modern one to better suit the medieval feel of the Lord of the Rings.