Ampere's Law describes the direction of a magnetic field around a current-carrying wire. The magnetic field encircles the wire in the direction defined by the right-hand rule. Point your thumb in the direction of the current in the wire and curl your fingers. The direction your fingers curl is the direction the magnetic points as it curls around the wire.
These apparatuses employ small compasses to demonstrate the direction of the magnetic field at certain points along the wire. With no current flowing through the wire, all compasses point toward north (more specifically, toward the Earth's magnetic south pole).
When the current is turned on, the compasses align according to the magnetic field as it circles around the wire. Note that the current goes in through the red wire and out through the black.
There is also a version of this apparatus that can be used with an overhead projector.
One shortcoming to this design is that the magnetic field at the compasses has components from both the vertical and horizontal wires, so it is not as clear of a demonstration as the other apparatus.