What causes notches in elephants' ears?
A natural process is something quite vague: this is a natural process, but it's not related to the elephant's ageing. Neither is it (normally) related to fighting.

Those notches and tears are caused by the daily activities of elephants, feeding in the bushes. The longer the ear, the more prone it is to damage. On the other hand, thicker ears are less prone to damage.

Day by day, the number and pattern of tears/notches/holes changes. 

Curiously, this pattern of tears/notches/holes is used by researchers to identify individuals. Not only that, but also the pattern of the veins in the ears (you can see them in the left ear):



Thus, the same way the tail of a humpback whale or a human fingerprint is unique to each individual, so are the elephants' ears.

Sources:


http://voices.nationalgeographic.com/2013/08/16/name-that-elephant-how-to-identify-elephants-in-the-wild/
https://www.elephantvoices.org/support-now/814-how-to-use-ear-notches-and-tears-to-id-african-elephants-.html