"If the system A is in thermal equillibrium with a system B and the system B is in thermal equillirium with a system C, then the systems A and C are in thermal equillibrium with each other."
The law tells us something about the nature of thermal equillibrium. Since the thermal equillibrium of the pairs of systems A and B & B and C by itself means that A and C are in thermal equillibrium, it leads to an idea of a physical quantity which is the same for two systems in thermal equillibrium. The physical quantity is temperature.
The reason for calling it the zeroth law of thermodynamics is that while it was recognized as an important law of thermodynamics much after the three other laws were widely known, it was percieved to be more fundamental than those other three.
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