The snake is one of the seminal animals of Tai-Chi. The imagery is of a snake (duh) wrapped around a tree branch, lowering its head, and about to strike.
As with many Tai-Chi postures there are a variety of very different ways of performing this based upon what lineage you are talking about. In the traditional Yang style it appears twice, but both times on the same side, with the left leg leading. In the Beijing 24 style it also appears twice, but on alternate sides. To the untrained eye some don’t even resemble one another. But regardless… I happen to think that whilst this move might not have the most realistic martial applications that it is one of the coolest looking postures, and fun to do, although difficult.
Also common to many Tai-Chi postures is that they can be applied from both a defensive and an offensive perspective. From an offensive standpoint you wrap and adhere to your opponent whilst sinking low to attack their lower body. As a defense it allows one to evade strikes and leads the opponents arm (or leg) into an advantageous position for you and allows you to advance to offensive counterattack positions like Step Forward to the Seven Stars, or Golden Rooster Stands on One Leg.
Modern fighters are often very quick to dismiss Tai-Chi outright, or at least certain postures. One of these critiques around Snake Creeps Down is that it leaves one’s head very vulnerable to kicks. Maybe so; but such criticisms and commentary miss the whole essence of Tai-Chi.
One major difference between styles that appears, is how low one goes with the technique. Another notable variation is how much forward lean there is with the torso and upper body. The following classic photos clearly illustrate these differences.
As you can see there is a whole lot of different ways of doing this. In fact if you look at the last two pictures it’s interesting to note that they are father and son. Some teachers additionally allow for varying the stance(s) based upon the physicality and suppleness of the student. No way is right or wrong, within the context of the style. Not better. Not worse.