So at one extreme, the liquid is moving along with the sliding plate and at the other extreme the liquid is perfectly still.
There also ought to be some friction between the moving plate and the liquid that will make the liquid move along at the same speed as that plate. What happens to the liquid between the plates? There ought to be some friction between the stationary plate and the liquid that will keep the liquid still. One plate says still and the other one moves. One of the common ways of assessing properties in rheology is to place a sample between two parallel plates and move one plate with respect to the other. There's an element of force or pressure that comes into play here, too. Another very simple definition, attributed to chemical engineer Chris Macosko at University of Minnesota, is the study of 'what happens when you squish stuff'.
Rheology is, literally, the study of flow. Viscosity measurements are the realm of a field of science called rheology.