They are generally depicted as very large, powerful-looking white tigers (also called "albino tigers").
Tigers are generally patient stalkers when hunting for preys, and their personality might reflect that habit. It is also ferocious and won't back off from a fight if they think they can win. Not much is known about their personality in general, but one could assume that they would dislike Oni, since those tend to wear clothes made out of Tiger skins, as well as Dragons, from some legends.
During the Han Dynasty (in China), people believed the tiger to be the king of all beasts. Legend had it that when a tiger reached 500 years old, its tail would turn white. In this way, the white tiger became a kind of mythological creature. It was said that the white tiger would only appear when the emperor ruled with absolute virtue, or if there was peace throughout the world. Because the color white of the Chinese five elements also represents the west, the white tiger thus became a mythological guardian of the west.
According to the Chinese Annals of Wu and Yueh, three days after the burial of the king, the essence of the element metal assumed the shape of a white tiger and crouched down on the top of the grave. Here the tiger is a protector - a preserver. The male tiger was, among other things, the god of war, and in this capacity it not only assisted the armies of the emperors, but fought the demons that threatened the dead in their graves.
In some legends, it's archenemy is the Dragon.