Hobbing is a method of cutting gears with a cutter that is similar to a worm (helical threaded screw). Naturally, the worm thread of the hob is cut parallel to the helix axis with gashes to create cutting tooth faces. These teeth are also relieved (given a few degrees of clearance) behind the cutting face, so that indeed, it can penetrate the work and make a cut.
A hobbing machine is a specially constructed machine which can utilize this type of tool.
Hobs can generate worm wheel teeth, spur gear teeth and helical gear teeth. The hob "pulls" itself along the gear OD, just as a worm pulls itself along a worm gear. The external gearing ensures that the hob and workpiece rotate at the correct rate so that only whole numbers of gear teeth are generated on the new gear.
The hobbing machine permits the hob to be run at various angles to the axis of the new gear. Because of this, the hob can generate worm wheel teeth if it is run at 90 degrees to the new gear, or it can cut spur gear teeth if it is run at an angle equivalent to its own helix angle, neutralizing it, in effect. It can also be run at other angles to generate helical gear teeth.
For spur and helical gear cutting, the gear blank is also feed axially along its own axis, so the the hob cuts across the entire face of the tooth. For worm wheel cutting, the hob remains stationary over the center of the wormwheel blank. This creates the unique shape of the worm wheel tooth, which is non-interchangeable with another worm wheel. Worm wheels and worms run in paired sets only.
That's it in a nutshell.