The main subject is mudras - hand gestures, by means of which the actor/dancer communicates with the spectator. Communication through mudras is in some way trying to use the potential of connection of form or similarity of objects between gesture and its meaning, or the real original.
The author is comparing two lines, which have a common origin, but during about two thousand years of development, they became two different streams representing two different traditions. On the one hand there is the bharatanatyam which is wide-spread globally nowadays, and on the other hand the kathakali and kūdiyāttam which are known in the area of Kerala.