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.
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 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.
They have done the same thing with chimpanzees and elephants and it's really cool to watch the videos. You see the chimpanzee try to attack its reflection at first, but then it slowly figures it out and starts grooming its hair and checking out its teeth and stuff. (And then peeling the sticker off its forehead.)
Here is a series of YouTube videos on this:
http://youtube.com/results?search_query=mirror+self-recognit...
Aside from the usual stuff humans like about some animals, like pair bonding, raising their young and living as a family, and being very social with each other and even other species (including humans), there are a lot of other human-like traits of elephants. Elephants have astonishingly long memories (it's a wives tale that turns out to be true). They'll pause on the spot where loved ones have died, even many years later, and groups will console each other after a loss--having a funeral of sorts. They remember humans who have been cruel or kind to them in the past, and behave accordingly. They communicate vocally and are known to express a range of concepts this way--not just warnings, but also greetings, calls, and "names" (unique identifiers specific to each elephant). And, recently humans "asked" elephants to carry cameras into the forest for them, to help study tigers. Since elephants and tigers are on peaceful terms (what's a tiger gonna do to an animal that could crush it with one foot?) it worked well, and some amazing footage resulted.
Given all of this, it shouldn't be at all surprising that an elephant could be trained to paint a particular picture. It is rather unfortunate that it takes something like this to impress tourists of the intelligence of one of our closest intellectual peers, when elephants have so many more fascinating traits and ways of exhibiting impressive intelligence.
The video is interesting but misleading. I would highly doubt that the elephant has a clue as to what it's painting. Elephants have an incredible memory and amazing dexterity, those two things coupled together makes it likely that the elephant is painting from memory. The elephant also demonstrates some advanced painting skills that i'm sure it was taught. I would be more impressed of some cave paintings done in wild naturally by animals.
That being said, it's still a pretty neat video.
