This is a critical skill on motorcycles, and most people learn it subconsciously, but real masters can throw the bike into turns in ways that make no sense unless you take countersteering into account. I'd love to be good enough someday to make physics seem confusing...
As a cyclist and motorcyclist, I've always found that bicycles will let you get away with not knowing you're countersteering, but on motorcycles you really need to be explicit about "push harder to turn tighter".