Described by various people as a snake image, the above graphic appears on the Apple Watch screen when it has thoroughly run out of battery power. You might even see it on a new Apple Watch just out of the box.
People get a little confused after hearing this answer, because even after they attach the power the image might not go away for a while. The Watch charges relatively slowly due to inductive charging, and the Watch won’t get enough juice to resume normal service for several minutes. Just give it time. If you see the logo even after a few hours’ worth of charging then it’s likely the battery inside the Watch is dead, and you should consult your nearest Apple Store.
I’ve seen this question asked repeatedly on help forums, so I hope this provides the answer.