The main characteristics of the elephant are his strength and steadfastness. Therefore it become a symbol of physical and mental strength, as well as responsibility and earthiness.
In Indian mythology... white elephants are considered very special... elephants were considered to bring good luck and prosperity...
In buddhism the elephant is a symbol of mental strength. At the beginning of one's practice the uncontrolled mind is symbolised by a gray elephant who can run wild any moment and destroy everything on his way. After practising dharma and taming one's mind, the mind which is now brought under control is symbolised by a white elephant strong and powerful, who can be directed wherever one wishes and destroy all the obstacles on his way. ◼ Symbolism of Animals in Buddhism
In Buddhism, White is representative of the principles of purity, as in Western Culture, but it is also considered the colour of knowledge and longevity. It is consider a colour of extremes, associated with the cold of snow and the smelting of metal. White is associated with the Buddha Vairocana. According to Buddhist legend, Buddha's mother, Maya, dreamt of a white elephant touching her right side before Buddha was born. Elephants, associate with rain clouds and fertility, are seen as good fortune, and following that the elephant was white meant purity and learnedness for the child. Because of this dream, seeing a white elephants spells remarkable fortune, which holds truth whether in reference to mysticism or not, as they are quite rare. The white elephant is thought to be Buddha descended from the heavens. ◼ Colors of Religion: Buddhism (info and image source)
