Watch this. It's intriguing.
I searched around the internet to see if this video is a fake. Is the elephant really painting? I think she is, but apparently people train elephants in Thailand to paint representations like this. (which is still amazing). I would guess that's what happening here, since it's a bit too cutesy to imagine the elephant choosing to paint herself holding a flower.
It's a tourist gimmick, probably. I bet that painting was for sale to all the oohing and ahhing people in the audience....
Hopefully the money is at least going to provide an elephant sanctuary.
On their own, some elephants do like to paint, but rather abstractly I would think.
Elephant Paints Self-Portrait
Above, some 'real' elephant paintings