Darkfield involves lighting the subject from below (through glass/perspex/whatever), with the lights moved out to the side so that they shine up at the subject at a 45 degree angle. The camera is positioned vertically above the subject. This means that the lights do not shine directly into the lens - only light that is caught by the subject and diffracted upwards enters the lens. Hence the silhouettes with a dark background.
It's also used a lot in microphotography, but the technique is a bit different.