The BBC micro:bit is a pocket-sized computer that introduces you to how software and hardware work together. It has an LED light display, buttons, sensors and many input/output features that you can program and physically interact with. The latest micro:bit adds sound sensing and playback capabilities.
You might also hear the micro:bit referred to as a microcontroller. The board contains a microcontroller that can be programmed to perform specific tasks, but it also has input and output devices like buttons and an LED display which makes it more than a microcontroller.
A microprocessor plus memory, storage and physical input/output devices make a computer like the one you are reading this article on. The micro:bit is just a pocket-sized one.