If knowledge is power then power is, well, pretty darn great. Especially if you're in the market for a diamond. With so much subjectivity in the marketplace, cut is one of the more clearly defined concepts. Phew.
For any traditional cut - think round, emerald, oval, cushion, etc - you have the same basic anatomy of the diamond. This includes the table which is the flat surface on the top surface, the girdle which marks the widest part of the stone and diameter, and the culet which is the pointy bit at the bottom.
Every gemstone has very strategically placed facets, this is to increase the reflectivity. The facets are carefully cut to bring out the natural brilliance. If a stone is cut too shallow or too deep, light will reflect back at different angles. This can make the gemstone appear grey or smaller than it is. In an ideal cut stone, you're looking for perfect symmetry.