One of the most popular depictions of the elephant is through the Hindu religion. The god Ganesha is easily identifiable with his large elephant head on a human body. His likeness will be found across South Asia in countries like India, Nepal, and Thailand. Ganesha is a patron of the arts and sciences and looked upon as the remover of obstacles. A steadfast god to look to in times of trial.
In Buddhism you will find the presence of the elephant pair Kangiten, represented as male and female elephant headed humanoid figures embracing as a symbol of the unity of opposites. Enforcing the belief of the oneness of all things though they may be seemingly different.
The elephant is not indigenous to Europe but was discovered through their exploration or Asia. Awed by the ferocity of the war elephant in battle, Europe adopted the beast as a symbol of militaristic strength. Napoleon even commissioned a giant cast bronze elephant fountain to be made from guns confiscated in victorious battle. The fountain was never completed (hello Waterloo).
America adopted the elephant to represent the Republican party in 1884. The origin is a political cartoon done by Thomas Nash. The elephant is shown charging in dispersing other smaller animals representing other political interests at the time. Another account of dominance and strength.
Lastly Elephants are native to Africa and usually where most people imagine them. In Africa the elephant is revered for its strength, wisdom, and memory. The elephant was depicted on several coat of arms throughout time in Africa including South Africa, The Ivory Coast, the kingdom of Laos, and the kingdom of Dahomey.
Globally you can see the elephant is respected and admired for it's strength, it is looked to for it's wisdom, and it is a symbol of conquering obstacles and embracing change.