The CPU – a highly complex silicon chip ranging from the size of a matchbook to the wallet-sized Intel Xeon – is your computer’s brain, taking requests from applications and then processing, or executing, actions, a.k.a. operations.
The faster your processor, the more operations it can execute per second. The more operations you have per second, the faster things happen in your applications; thus, games play more smoothly, and spreadsheets calculate more quickly.
Sometimes the term CPU is also used to describe the whole box that contains the chip (along with the motherboard, expansion cards, disk drives, power supply, and so on). Both uses are widespread, but only the first is really accurate.