In layman's terms, it provides very low frequency bass. A woofer provides bass, so the subwoofer provides the lower frequencies that the woofer does not. A tweeter provides the high end, and a mid-range provides the sounds in between.
A subwoofer will provide a nice low bass sound for drums, bass violins, and the like. It provides the nice rumbly bass.
All too often, subwoofers in cars get misused to create bone-jarring bass that makes the brake pedals of the driver behind them vibrate and their stomach queasy. To my ears, a good bass sounds clean not necessarily loud.