Some process in which a thermodynamic system goes from an initial state i to a final state f. During the process the system absorbs heat Q from the surroundings and performs work W on it. If system and surrounding are not capable to return their initial state process known as irreversible.

The spontaneous processes of nature are irreversible.

The base of a vessel on an oven is hotter than its other parts. When the vessel is removed, heat is transferred from the base to the other parts, bringing the vessel to a uniform temperature (which in due course cools to the temperature of the surroundings). The process cannot be reversed; a part of the vessel will not get cooler spontaneously and warm up the base. It will violate the Second Law of Thermodynamics, if it did.

The free expansion of a gas is irreversible.

The combustion reaction of a mixture of petrol and air ignited by a spark cannot be reversed.

Irreversibility arises mainly from two causes: one, many processes (like a free expansion, or an explosive chemical reaction) take the system to non-equilibrium states; two, most processes involve friction, viscosity and other dissipative effects.

Since dissipative effects are present everywhere and can be minimized but not fully eliminated, most processes that we deal with are irreversible.