There are many surfaces in Okami which Ammy can stand on, but which will constantly push her in some direction as long as she remains grounded. These slippery surfaces (often slopes) can often still be traversed by jumping across them. Ideally, you would repeatedly jump the instant you touch the ground to minimize the time Ammy is pushed. This is called greenhopping, after the splash of green vegetation that appears whenever Ammy lands.
Some surfaces are seemingly more slippery than others, pushing Ammy off very quickly. In some cases, Ammy will not even be able to land on a slope unless she has enough downward velocity (i.e. has been falling a long enough distance). If Ammy doesn't meet the threshold for landing on a given surface, she will be pushed down the slope while remaining airborne. In these situations, air-tackle bounces are often used to gain enough height to land and greenhop. This can be seen in Fireburst Early.
Any instance of traversing a slippery surface can technically benefit from greenhopping, but notable instances where doing so is key include: