An important property of temperature is that when two objects of different temperature are placed in contact, energy will move from the warmer to the cooler. When we say about thermal equilibrium of a system, consider that the system does not exchange energy with the rest of the world. Then energy moves around within the system until thermal equilibrium is reached.  When we place a thermometer in contact with body and wait for equilibration to occur. It is important that equilibration takes place, and that result is objects at the same temperature: if objects in contact could stay at different temperatures, a thermometer might also never come the temperature of the object it is touching, and we would have no way to measure or even define the temperature of anything.