An example of a partial order that blew my mind recently are the ordering of "events" in special relativity. Two events can be ordered in time (i.e A happened before B) if their spacetime interval is positive. But for two events that are separated by a distance than light can't travel in the time by which they are separated, then nobody can give a before/after order to these events.
This fits exactly into the partial ordering system.
This fits exactly into the partial ordering system.