Equilibrium state:
A system is said to be in thermodynamic equilibrium if it satisfies the condition for thermal equilibrium, mechanical equilibrium and also chemical equilibrium. If it is in equilibrium, there are no changes occurring or there is no process taking place.
Thermal equilibrium:
There should not be any temperature difference between different regions or locations within the system. If there are, then there is no way a process of heat transfer does not take place. Uniformity of temperature throughout the system is the requirement for a system to be in thermal equilibrium.
Surroundings and the system may be at different temperatures and still system may be in thermal equilibrium.
Mechanical equilibrium:
There should not be any pressure difference between different regions or locations within the system. If there are, then there is no way a process of work transfer does not take place. Uniformity of pressure throughout the system is the requirement for a system to be in mechanical equilibrium.
Surroundings and the system may be at pressures and still system may be in mechanical equilibrium.
Chemical equilibrium:
There should not be any chemical reaction taking place anywhere in the system, then it is said to be in chemical equilibrium. Uniformity of chemical potential throughout the system is the requirement for a system to be in chemical equilibrium.
Surroundings and the system may have different chemical potential and still system may be in chemical equilibrium.