Terminology
The microcanonical ensemble is a specific instance of a more general construct, the statistical ensemble, a theoretical tool used to analyze equilibrium systems given by specified macroscopic variables. A given ensemble provides a complete description of all of the accessible microstates of the system. The microcanonical ensemble is distinguished from other ensembles by its specifying macroscopic variables being the number of particles (N), the volume (V), and the total energy (E).
The ensemble is a set of microstates. Each microstate is a complete description of a possible state of the system. In classical mechanics, the microstates of a gas would be represented by the position and momentum of all of the molecules, which in principle specifies all possible degrees of freedom. In quantum mechanics, a microstate would be the composite and complete many-particle wavefunction.
In classical statistical mechanics it is impossible to determine the microstates of the system because all properties of the system are continuous, not discrete. This issue is resolved in quantum mechanics via the use of eigenstates, which are discrete. However, the ensemble approach bypasses these by bundling all microstates that lead to the same macroscopic properties such as volume, temperature or energy in a macrostate.
A statistical ensemble describes this macrostate in terms of all of its microstates. The fundamental postulate of statistical mechanics states that, for a given macrostate of a given equilibrium system with specified macroscopic variables, all accessible microstates are equiprobable. To fully describe a statistical ensemble it is also necessary to specify the probability for a certain microstate to occur, so this postulate circumvents that issue. Thermodynamic properties of the system are then obtained by taking the average value of all microstates in the ensemble.
Read more about this topic: Microcanonical Ensemble