Physical signals can not propagate faster than light. The causal ordering is the time ordering of events that could in principle be connected by physical signals. The causal set programme is based on the idea that if space-time is discrete, then the causal ordering is all the structure needed to construct a theory of gravitation with general relativity as its continuum limit.
Our present theories are based on concepts of particles and fields that are objects living in a background continuous space-time. The basic concepts of a discrete theory must be some kind of fundamental events, and space-time is nothing but the causal ordering between them. We have no idea what these fundamental events are, and how to formulate a dynamics.
Experimental input would be very useful, but the discreteness scale is most likely the Planck scale, which is far below what is accessible today.
(The slides will be available here)