It is always curious to see cats drinking without ever getting their chins wet. Their tongues go up and down, but their faces stay dry. Up till now the theory was that they formed a sort of reversed ladle with their tongues to spoon the water or milk up into their mouths. That is, their tongues curled back towards their lower teeth and up to make the ladle, which then rose and tipped the liquid into the mouth. Observation, photos and video seemed to bear this out more or less.
Now there has been much more careful investigation by Pedro Reis and his team at MIT, in the Elasticity, Geometry and Statistics Laboratory, where the mechanics of thin objects - like cats' tongues! - are studied. Some fascinating videos are available from the team here which show what is really happening when a cat drinks.
It seems that the flattened end of the dorsal (top) surface of the tongue touches the liquid, and is then drawn up, taking some liquid with it due to adhesion and surface tension. Some of the column of liquid gets as far as entering the mouth because of inertia, but would soon fall under the influence of gravity, were it not for the cat snapping its lips shut and trapping some in its mouth for swallowing. It's too complicated for words, but look at the videos, and the video of a mechanical illustration! That makes it clear - as does trying it with your own tongue and lips!
Needless to say some popular newspaper articles have suggested that because cats can do this so skilfully they must be capable of complex mathematical analysis. Oh, well. It seems that other members of the cat family must lap in the same way, judging by the speed of their tongue movements.