A DC clampmeter works on the principle of the Hall Effect. The Hall Effect, named after Edwin Hall who discovered it 1879, states that when a conductor carrying current is placed in a magnetic field, a potential is induced across the conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current. It is caused as the charge carriers, electrons or holes, experience a force known as the Lorentz force and are pushed to the sides of the conductor.
A clampmeter which works on the Hall effect has a sensor known as the Hall element. The Hall element is subjected to the magnetic field caused by the flow of current to be measured. This causes a small voltage across the Hall element. This voltage is amplified and measured.
images courtesy: commons.wikimedia.com