What is a "kiln mark"?
A kiln mark is a small, dimpled mark that appears on the bottom of a lot of older pottery and china pieces. The mark is caused by the points of the rack or pins that held the piece inside the kiln while it was being fired. Some kiln marks are barely visible, while others can be somewhat discolored and rough.
What is a "glazing flaw"?
A glazing flaw is a flaw that occurs during the production of a piece of china. Glaze is liquid when applied, and it can drip and bubble like paint. Sometimes bits of dust or stray bits of clay will be trapped under the glaze, or the glaze will leave a small bare spot. There are a lot of flaws that can fit in this category, but they're usually small and not very noticeable. Kiln marks are often considered glazing flaws, since they cause a disruption in the glaze.
What is "crazing"?
Crazing occurs when the underlying clay of the piece of china shrinks sometime after the piece is glazed. The glaze doesn't shrink with it and cracks under the stress of the shrinkage. Shrinkage occurs when the clay loses moisture and can indicate that a piece was improperly fired (wrong temperature, not fired long enough, etc...).
You see crazing often on older pieces, however, since age can cause the clay to dry out and shrink, and because older production techniques were not as precise as the ones we have nowadays. Today we have much finer control over temperature and moisture content, so crazing is less common.