Sometimes it is not easy to visualise contours surrounding a peak. An equivalent way to think of prominence is to imagine an island being flooded.
If the island is flooded to the point where Peak A and Peak C are just separated on different islands, the prominence of C is its height above that flood level.
The point at which the “flooding” separates the islands is of course the key col between A and C.
If the flooding were extended further to the point where peak B was just separated on a different island to C, then B’s prominence would be its height above that flood level. This is equivalent to the height above the key col between B and C.