I don't understand the concept of phase diagrams?

[PhyIsOhSoHard]

Let's use the material brass as an example.

My problem is that I have no understanding of the concept of "phases". In the phase diagram for brass, we have α, β, γ, δ, ε, and η phases as well as the liquid phase (L).

My question is, how do I interpret these phases? What is the difference between the phases?
If I have a brass material that consists of the α + β phase, what does that then tell me? And how is that different from the γ + δ phase?

My textbook does not give any good explanation about this.

 

[NascentOxygen]

Different phases have different arrangements of atoms of the constituent elements. These atoms are arranged or clustered together in precise arrangements, not just stuck together haphazardly. Different microstructures will lead to the alloy showing different properties.

EDIT: I didn't notice this pdf file was so large. Perhaps search on google for something smaller.

http://vector.umd.edu/links_files/H3 - phase diagrams tutorial.pdf