Climb cutting is a shaper technique that is often overlooked. I have always thought that the reason for this is that climb cutting cannot be done safely without using a power feeder and for some reason, many shops have shapers that are not equipped with these important accessories.
Climb cutting is simply feeding the material in the same direction as the cutter rotation. It is horribly unsafe to attempt by hand because the cutter will act like a driving wheel. On even a small machine with "only a few" horsepower, there is no way that even the strongest person could resist the force of the cutter's pull.
Climb cutting is done primarily on the shaper, a machine that has been described as a device used for throwing pieces of wood across the shop that are too heavy to be thrown by hand. There is little point in climb cutting on any saw. But when you are attempting to shape a highly figured piece of wood (or many), climb cutting can eliminate the inevitable chipping, splintering and tearout that can render an expensive and beautiful board useless.
Climb cutting can also be done with a router but only if the router is hand held, not mounted in a table (again unless a power feeder is used). The router itself can be gripped firmly enough to make climb cutting "relatively safe" if light cuts are taken. But in a table, even a small router can generate enough force to turn your stock into a missile. I have a small 1/4-hp feeder mounted on my router table and this allows me to climb cut on it in the rare moments that I opt to use the router table instead of the shaper.