The primary function of a cache in computer systems is to temporarily store frequently accessed data to improve system performance. By keeping copies of this data closer to the CPU, caches reduce the time and resources needed for data retrieval, boosting overall speed. Caches can be classified into various levels, such as L1, L2, and L3 caches, with each level having different speeds and sizes. This hierarchy helps balance cost, speed, and efficiency, ensuring that critical data is readily available when needed.