This is the technical name (and the common name, in so far as there is one), for the little "dip" on the side of your wrist that occurs when you put your thumb out. To find it, extend your thumb as if you are hitchhiking; this will raise the tendon down the back of your thumb. There will be a shallow dip on either side of this tendon; the dip on the outside (towards the edge, not the back) of your hand, down where your hand is just meeting your wrist, is your anatomical snuffbox.
For the Medical Students in the Audience
A hollow seen on the radial aspect of the wrist. It is bounded by the tendon of the extensor pollicis longus posteriorly and of the tendons of the extensor pollicis brevis and abductor pollicis longus anteriorly. The floor is formed by part of the dorsal surface of the scaphoid and the dorsal tubercle of the trapezium bones (the scaphoid may be used as a locater). It is crossed by the radial artery. The tendons forming the anatomic snuffbox become prominent when the thumb is extended fully. If you want to get really fancy, you can call it the Tabatière anatomique or the Fossa tabatière.
AKA the poor man's snuffbox.
wick reports that when he used snuff, he used his anatomic snuffbox as his preferred method. You knock your snuffbox against your thumb, and the snuff falls neatly into your anatomic snuffbox. This also has the advantage of making it easier to brush off the remaining snuff, keeping your fingers clean. When using the snuffbox for practical purposes, you don't make a hitchhiker's thumb, but instead extend the four fingers.