A processor receives input and provides output, handling calculations rapidly. Processors have cores that read and execute instructions, with more cores enabling more simultaneous tasks. The Core i3 is Intel's entry-level dual-core processor for desktops and laptops, while the Core i5 is the mid-range option with either dual or quad cores. Key differences are that i5 processors have higher clock speeds, support for hyper-threading, larger caches, and Intel Turbo Boost technology.