The wet cloth between the counter and the cutting block keeps the cutting block from sliding / moving on you when force is applied, which is more comfortable and safer.
I cook every day, and I’m also a mechanical engineer, I’ve never understood where the sideways force comes from. I’ve also never had a board slide away from me. Tbh I thought this came from chefs chopping on stainless steel worktop. I’d like to understand.
Even if you're chopping perfectly vertically, a board will slide around or rock slightly. Like say you want to julienne some basil or something with a chef's knife, you'd probably be doing a rock chop, which involves lateral forces, causing the board to slide. Then also if you want to scoop up the food with the side of your knife, like scrape up minced garlic, those are lateral forces too. A wet cloth under a cutting board also softens/dampens the force of the knife hitting the board when chopping, which is nicer on your wrists.
When you chop, you're applying force almost entirely vertically. When you slice, you're applying at least some force horizontally. That horizontal force can be transmitted through the knife to the food to the cutting board, causing the board to slide. It's especially noticeable when you're slicing food that is high, like a loaf of bread, and the cutting board is on a slick stone countertop.
