I'll try to answer this as simple as possible (but not simpler :-) )
Ask a number of people what they assume energy is. You will have as much different answers as the number of people. So, what is energy? Well, -energy is the capacity to do work- and this is available in a lot of different forms, p.e. electrical, chemical, potential, etc. However not all energy available can be transformed into work. Only a part of it can. Why is this so? Consider therefore a heat source of some kind. This heat can be used to do work and will cool down in doing so. However it can only do this until the temperature is equal to the surrounding, not to a lower value because you would need work in getting the temperature back up. The work obtained from the heat source until the temperature of the surroundings is the amount of exergy. This is a smaller value than the energy what was available in the beginning and the difference is the anergy, the part which is unusable. So in short: energy=exergy+anergy, with exergy the usefull part and anergy the unusable part.
In the process of transforming one kind of energy into the other we have an exergy loss. This means that during the process some exergy is lost and is transformed into anergy. Assume as a simple example that you have 100J energy of which is 80J exergy and 20J anergy in the beginning. After transforming this energy to another form of energy you still have 100J at the end, but only 40J of exergy and 60J of anergy. This means that 40J of exergy is transformed into anergy. A part of the usefull energy is tranformed into unusable anergy. The fact that the energy is constant is nothing more than the first law of thermodynamics. The loss in exergy is a manifestation of the second law. The fact that there is some amount of anergy in p.e. a heat source is the reason why we can't use the energy in the sea, it is all anergy, at least to some extent. To what temperature must we cool it down, it has already the temperature of the surrounding? A mistake often made. There is energy which is (almost) completely transformable into work meaning that is has no anergy, this is electrical energy, work itself is also exergy.
Exergy and anergy are related to entropy, the amount of entropy rise is related to the loss of exergy. That's one reason why understanding entropy is so important. Be carefull in using this, the entropy can drop in a part of a system, but must always rise for the complete system, often the surroundings entropy rises more than the drop of the system's part.
Hope this clears something. There's bound to be reaction to this post :-)