USPSA has a list/book of standard courses of fire with specific measurements and procedures. Everyone throughout the U.S. shoots these courses in the same manner and the results are submitted to USPSA. Typical monthly matches will include one Classifier stage. A Special Classifier match is comprised mostly, or solely, of Classifier stages.
Once you join USPSA, you need at least 4 classifier stages within any single Division (e.g. - Production, Limited, etc.) to receive a USPSA Classification (D, C, B, A, Master, Grand Master). The Classification is based on your performance as a percentage of the best scores. It can get pretty complicated to review all the policy details, but basically, you will know what percentage you shoot as compared to the best shooters in the country.
A Special Classifier match can get you the minimum 4 scores in one day rather than in 4 separate matches. It is a good opportunity for new USPSA members to receive an initial classification, or for members to receive a classification in a different Division than their usual choice.
Gary/HAS requires competitors to join USPSA after shooting a couple matches. This policy is for several reasons. First, USPSA recommends that some type of policy be in place. Also, the old digital scoring system would carry stored competitor information only if the competitor is a USPSA member (using the USPSA number). I am not as certain about the PractiScore format of storing info. And finally, it just seems appropriate that we should support the organization that forms the basis of this great sport.