When a system is not in equilibrium (or dead state in this case) with its surroundings there is an opportunity in convert this departure from equilibrium to do some useful work.
For example, if there is a difference between the temperature of system and surroundings then this temperature difference can be utilized to produce useful work with the help of a heat engine. If a pressure difference is present between system and surrounding then this pressure difference can be utilized to get some useful work with the help of a turbine.
Availability of a thermodynamic system
The availability of a given system is defined as the maximum useful work (total work minus PdV work) that is obtained in a process in which the system comes to equilibrium with its surroundings. Availability is a composite property which means that its value depends both on system and surroundings.
Dead state of a thermodynamic system
When a system comes in equilibrium to its surroundings, which means that the availability of the system is zero it is called in dead state. No useful work can be obtained from a system which is in dead state.
Nutshell: The maximum amount of useful work that can be taken from a system before it comes in equilibrium with its surroundings, is known as availability. Here one can note a term ‘Maximum amount of useful work’, which may cause a doubt.
Why not full amount of useful work?
The answer to this question is that the work done against the environment or surrounding is not a useful work to us, hence we subtract it from the total work obtained.
Another thing is what is dead state, a dead state is a state when a system comes in equilibrium with the surrounding. Since we can not derive work from a system which is in equilibrium with the surrounding, so it is called a dead state.