While brightfield microscopy illuminates the sample with a filled cone of light, in darkfield microscope the condenser is designed to form a hollow cone of light. The objective lens sits in the dark hollow of this cone and light travels around the objective lens, but does not enter it. The entire field of view appears dark when there is no sample on the microscope stage. However, when a sample is on the stage the sample appears bright against a dark background. It is similar to back-lighting an object in order to make it stand out.
Illustration courtesy of Washington State University.
The illustration above shows how the light is directed differently when using a darkfield microscope or a brightfield microscope.
There are several different types of darkfield microscopes, including stereo darkfield microscopes, darkfield biological microscopes and darkfield metallurgical microscopes. Darkfield is commonly used to better view bacteria, blood cells, diamonds and precious stones, and various types of algae.
You can learn more about darkfield microscopy and view different darkfield microscopes here.