Climb cutting is a technique where the rotational direction of the cutter or blade tend to pull the tool or wood into the cutter. This is generally considered unsafe and absolutely verboten with some tools and operations, like ripping on a radial arm saw. The cutter or blade can catch the wood and pull the wood into the machine, or in the case of a router, the router can jerk away from you and mess up your workpiece not to mention the safety hazards. This is why you make the cut into the rotational direction of the cutter or blade. There will be times due to required operations, techniques or situations where you have no choice but to climb cut. When you have to climb cut, a good & sharp cutter or blade will help avoid disaster, along with slow controlled feed rate and a firm grip on the wood or tool. Hope this helps.
