(2.1.3) Reining : One may distinguish different possible aspects in this question: What is the message of DFT? Why has it been successful? How is it used today? What distinguishes it from other theories that deal with the many-body problem? Some are treated later, so I think we should focus on the first aspect here. I also think that, in answering this and many other questions, a glance at other possible theoretical approaches is healthy, because we always learn from comparison, so let us try to have such a point of view whenever possible. The term DFT expresses the fact that observables in the ground state at zero temperature can be considered as functionals of the ground-state density. This can then be extended to thermal equilibrium etc., as others point out. So, it means that the density is a sufficient descriptor. It is important to say "can be considered as a functional of the density" and not "is a functional of the density", because this is a choice: observables can also be considered as functionals of the many-body ground-state wave function, or the one-body Green's function, or many other possible choices. The functional of the many-body ground-state wave function is very simple (whereas the wave function is not, of course), and a density functional will in most cases be exceedingly complicated (whereas the density is simple). Actually, I chose to say "can be considered as", because this does not imply that there must be an explicit expression.