Agate is the term for banded chalcedony. It is often found as the layers lining geodes deposited in different colors as a quartz geode formed contained different impurities (or even none, resulting in a white or colorless band).
As a general term, agate is so broadly descriptive that there are hundreds of names applied to varieties of agate from different localities. While many names reflect the source, some popular varieties are descriptive, such as "blue lace agate".
Note that in come cases, the term "agate" is used where the term "jasper" may be more accurate, as in "moss agate" in which a white quartz contains a fractal pattern of green and black, resembling tiny blades of moss.
Agate is primarily formed by the deposit of silica from solution; it is also a common method of fossilization, as the organic remains of some living thing are gradually replaced by quartz. "Agatized coral" from the Tampa Bay area is an excellent example, as are all of the specimens of petrified wood.
Agate is only one of several chalcedony (cryptocrystalline quartz) varieties. The primary varieties are as follows: