If two systems, call them A and C, are separate from each other, but they are both in equilibrium with a third system, B, then they are in equilibrium with each other.
This sentence, as written, seems (and is) believable.
However, it becomes more interesting when we discuss a consequence of it–things in equilibrium are at the same temperature, so the temperatures of things near each other tend to “equal out”.
Assume a room with two objects, one at 80 degrees F and the other at 60 degrees F. Gas particles bouncing back and forth around the room and hitting each other and both objects will give off energy or absorb energy until all the gas particles and both objects are the same temperature.
In real life these gas particles are bouncing off the walls of the building and those walls are influenced by the temperature outside of the building (which could be always changing), so we don’t try to tell you the equilibrium is going to occur at 70 degrees F.
Rob Sterling 