The primary float bowl is used to hold a quantity of fuel that will be aspirated into the engine for combustion. The primary or front bowl is the main bowl that feeds fuel into the engine. The secondary bowl, or rear bowl, is used as the need for more fuel increases. The secondary bowl is essentially not used when the vehicle is idling, and supplies the necessary fuel enrichment needed when accelerating. This type of configuration is not found on all brands of carburator, and is most commonly found on Holley carburators or those modeled after the Holly carburator.
For more info, see Your Guide to Tuning Carbs