The Canon Tripod Mount Ring A II (W)'s main purpose is to provide a better balance when mounted on a tripod. The 70-200 f/4 lenses do not require this ring to be mounted on a tripod - the camera body tripod insert can be used. But, this setup is front heavy. A top-notch ballhead can handle this load, but a lesser one will drop some amount after it is tightened. Care must also be taken to not tip the off-balance tripod forward. By moving the tripod mount to a centrally-positioned tripod ring (collar), balance is restored.
The advantages do not stop here. Since the tripod ring freely rotates, a nice amount of setup flexibility is gained. With the Canon Tripod Mount Ring A II (W) in use, switching from horizontal to vertical orientation is fast and easy. Otherwise, a major tripod head adjustment is required (such as dropping a ballhead into the drop-notch).
The thumbscrew tightens/loosens the tripod ring friction as needed. Simply rotate the ring to the desired position and lock it tight. If not needed, rotate the ring to an out-of-the-way position when not in use. Alternatively, loosen the tripod ring and pull out on the thumbscrew to completely release the ring from the lens. This release is accomplished via a hinge (noticeable in the pics). A hinged design allows the Canon Tripod Mount Ring A II (W) to be removed without the need to unmount the lens from the camera.
A tripod ring allow various accessories to be attached to the lens - flash brackets being one of the most popular. I use a Wimberley P20 Lens Plate on my Canon Tripod Mount Ring A II (W). This allows me to quickly mount the lens to any common Arca-Swiss-compatible quick-release clamp (Arca-Swiss, Wimberley, RRS ...) on a ballhead, monopod clamp, flash bracket ...
At one point, Canon had two Tripod Mount Ring A (W) models and one (B) model (W = White, B = Black). Both (W) models are shown in the pictures below (II is on the right), are interchangeable and are basically the same in their functionality. The II features a more-modern styling and a smaller thumbscrew (slightly more force required to lock it down).
The Canon Tripod Mount Ring A II (W) does not deliver the ultimate in tripod ring smoothness, but it works very well. Build quality is very nice. The features it delivers are worth the price to me.