It appears that the swan is picking up food or drinking from the top of the water. If it is dipping it's head, it is eating from below the surface. The other swan may not be hungry, but is still just hanging around the other swan. More than likely, the swan that is not currently eating, will eventually begin to eat and the behavior will be reversed in the pair.

If there are several pairs of swans or predators are in the area, the one swan may be on alert, watching in order to alert the feeding swan. This behavior occurs especially if there might be a territorial dispute among the swan pairs, if there are predators or the feeding swans are cygnets/ juveniles in which the parents will watch while the offspring feed.

The Regal Swan