Plywood grades are (in best to worst) - A, B, C,D for face (front) grades & 1, 2, 3, 4 for back grades. The lower the letter or number the better the material will be. All of our plywood is graded to the standards of the Hardwood Plywood & Veneer Association
A1, A2, B1, B2 is generally considered to be a good two sided product where both sides may be seen. Some blemishes are generally allowed on back side.
A3, B3, C3 are intended for use where one side will predominantly be seen but the other side needs to be reasonably clean, the back of items in this grade are generally good material but may have staining, less that acceptable veneer splices, scratches or other blemishes. This material works well for use as shelves, drawer sides & end panels
A4, B4, C4 are considered to be a good one side product where the back side will not be seen or it does not matter what is looks like. In A4, B4 or C4 the back of the piece may have open knots, filled knots, bad veneer seems or be of a different species that the front. This material will work well for drawer bottoms, covering of cabinet faces, bar backs & end panels.
CD is basically not to be seen.
Sorry, COOP
CDX is a softwood plywood and often improperly thought of as meaning exterior. That is not the case. "CDX Consists of a water-resistant bond and are designed for applications where long delays may be expected prior to providing protection, or where high moisture conditions may be encountered in service."
The real problems with lower grades of plywood are that they are not dimensionally stable. The thickness is not even and the veneer on the face is very thin And the lower the grade the less you can adjust this by sanding.
Here are links to more fully explain the differences and help you decide based upon your needs, and finances.
For Hardwood designations see:
http://justwoodworking.com/charts/hardwood_plywood.php
For Softwoods see:
http://www.awi-wa.com/_hidden/apagrades.htm