Thermal equilibrium happens when objects reach the same temperature and heat stops flowing. Scientists discovered this law after writing the first and second laws of thermodynamics. They realized this simple idea was the true starting point for the whole field.
They named it the zeroth law so it would logically come before the others. This fundamental rule gives us a scientific reason to trust thermometers. Think of a standard thermometer as the third system in the rule.
You place a thermometer in a beaker of hot liquid to measure it. Heat moves until the thermometer and the liquid reach the exact same temperature. You move that thermometer to a second liquid and the reading stays the same.
This tells you the two liquids share the exact same temperature. They would not exchange any net heat if you mixed them together. A common student mistake is thinking equilibrium means heat completely stops moving.
Heat energy actually continues to move back and forth between the objects. It just moves at the exact same rate in both directions for a net change of zero.