A Dobsonian, named after its creator John Dobson, is a reflector telescope, which means it uses mirrors, not lenses to capture and direct light. Generally, the two mirrors are a primary parabolic mirror and a flat secondary mirror. The design is an open-ended tube with the focuser for an eyepiece on the side at the top of the tube. Unlike the typical Newtonian, the Dobsonian is not mounted on a tripod.
The Dobsonian sits on a rocker style alt-azimuth mount. This mount allows for manual movement up and down (Altitude) and east to west (Azimuth). Compare this to the equatorial mount of typical Newtonians.
For more info on Dobsonian telescopes, check out our article on the advantages and disadvantages of Dobsonian telescopes.
