The zeroth law is incredibly important as it allows us to define the concept of a temperature scale.
If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.
For example, consider two separate cups of boiling water. If we place a thermometer into the first cup, it gets warmed up by the water until it reads 100°C. We now say that the thermometer is in thermal equilibrium with the first cup of water. Next, we move the thermometer into the second cup of boiling water, and it continues to read 100°C. The thermometer is therefore also in thermal equilibrium with the second cup of water. Using the logic of the zeroth law, we can conclude that the two separate cups of boiling water are in thermal equilibrium with each other. The zeroth law therefore enables us to use thermometers to compare the temperatures of any objects we like.
Why call this the "zeroth" law you may ask? The truth is that the other thermodynamic laws (the first, second, and third) had already been named by the time this one was formulated. However, scientists thought that it was so important that it should go before all the others, and hence it was termed the zeroth law