Also called "vriksha-asana" (vrik-shah-sa-na, literally "tree posture") in Sanskrit.
I was introduced to the tree pose by Wii Fit, the balance board fitness game for the Nintendo Wii. It was one of several yoga poses included in the game, demonstrated by a 3D animated trainer and judged based on how well the player can keep his balance on the board. As with most other balance board yoga poses, the screen displays a small circle which represents an acceptable boundary for your balance, and a red dot moves around (hopefully staying within the circle) as your weight shifts slightly while holding the pose. More advanced levels require you to hold the tree pose longer. The tree pose is considered a basic yoga technique.
There are apparently a few different variations on the tree pose, but the most common appears to be the one demonstrated in Wii Fit. Start by folding your hands in front of you, then bring one foot up to press its sole against your opposite inner thigh, and finally bring your folded hands above your head. Your raised leg should be held to the side, not the front. Hold for the desired amount of time (30 seconds is good for a beginner, I use 1 minute), breathing deeply. Repeat with the other leg.
While holding the pose, try to hold your head high, keep your back, leg, and posture straight, and breathe deeply. Do not hold your foot directly on your balancing leg's knee. Depending on your pants, you may have trouble holding your foot against your thigh. I find it works best if you wear shorts and have bare feet (no socks) for maximum friction.
/ \ (elbows should not
\o/ actually be bent)
|> (knee out to the side)
Standing on one leg is tricky, and potentially dangerous if you fall on something. To help get the hang of it, you can have a friend steady you, or stand near a wall and rest one hand on it. You may also find it easier to rest your raised leg lower on your balancing leg, lifting it higher as you get better.
The benefits of yoga vary widely depending on who you ask and how much they accept eastern mysticism, but the tree pose certainly strengthens and tones the legs and back, and improves coordination and balance.