Amazing... does anybody have any more information about this? Is this a trick where an elephant gets trained for many years to draw images, and gets used to the actions of moving the paintbrush across a canvas in a particular way (still an awesome feat)? Or do elephants naturally have drawing skills? Is there evidence that wild elephants draw things on cave walls, etc. by scratching on them with rocks or something?
Most likely, operant conditioning was used to build the behavior-set over time. There are 3 different videos where the elephant is painting the same picture, a raised trunk holding a flower, on different canvases and the elephant always starts with the same line.
Operant conditioning uses small rewards with increasing requirements to build behaviors. At first the elephant got a peanut for picking up the brush, then only for swinging it by the paint, then only for dipping it in the paint, etc.
The elephant likely does not have any conception of what it was drawing; most animals can't mentally translate abstract 2D images to 3D. Even humans, if they do not develop perspective during a critical period (if you were trapped in a small room for years, for example), will not understand perspective correctly.
The funny thing is that the elephants probably wouldn't regard this as particularly intelligent behavior. Well, except to the extent that a stunt that gets you peanuts can't be all bad.
On the other hand, if some elephants managed to use operant conditioning (and a special prosthetic, like a big drum) to teach a human how to subsonically tell another elephant ten miles away that the herd is gathering near the water hole, that human would be the star of the elephant world. The elephants would gather round to marvel at the human's astonishing front feet -- they aren't really very strong, but they can pick things up with their toes, almost as if they were using a trunk!
I also think this is a case of nothing more than operant conditioning.
I once saw a demonstration of how they trained a mouse to navigate an obstancle course (supposed to be a cross-section of inside a house wall with joists and so on) for some movie. When trained, the course took the mouse about 20 seconds to run and it looks like it must be one really smart mouse. But really, it learnt the route one step at a time over a period of days. I suspect a similar technique is used here.