A Central Processing Unit (CPU) or ‘processor’ is a phone’s ‘brain’. Generally speaking, the more processor chips a phone has, the faster it will be. In other words, a dual-core processor chip can process faster than a single-core processor chip. However this is sometimes at the expense of battery life.
A single-core processor has one chip, a dual-core processor has two chips, a quad-core processors has four chips, and octo-core phones have eight chips. If you use the smart features on your phone a lot, then ideally you'd have a phone with at least a quad-core processor.