Named after John Dobson, the inventor, it has revolutionized Amateur Astronomy by making large-aperture telescopes (some are up to 3 feet in diameter) relatively cheap and accessible.
It's characterized by having both bearing's axes pass through the center of mass, making it stable, at any size, and quite easy to operate.
It is an altitude-azimuth (Altazimuth) mount; the bottom axis is vertical (the azimuth bearing), allowing the base to rotate horizontally, and the other bearing, atop the base, is horizontal (the altitude), allowing the telescope tube to point up and down.
Though not as easy to attach to a clock drive (like the equatorial mount, with one axis parallel to the axis of the earth), it doesn't suffer the disadvantages of the equatorial mount: Heavy, hard-to-haul counterweights, which often create vibrations in the tube, and hence, the image.
John Dobson invented this mount while a Monk in Fenton, Michigan. Being rather poor, he had to make do with what he could find. To create his telescope, he ground the mirror himself out of port-hole glass, and fashioned the tube from a concrete pillar mold.
For many years (after leaving the monestary), he traveled the US, teaching classes on how to build a cheap telescope. For little more than the price of the materials, people would learn how to make a telescope, with the added benefit of keeping it when they were done.
He also gave star tours, using a 36 inch aperture scope, with a tube about 20 feet long, that he hauled around in a VW minibus. With such a large aperture scope, even the bright city lights didn't prevent seeing dim deep sky objects.
Every major manufacturer of telescopes now offer at least one model of dobsonian mount scope, since the amateur astronomer on a budget will get the most light gathering power per dollar spent with a dobsonian scope.