OK, maybe you have to use your imagination to see a computer mouse looking like a furry mouse.
But Mouse is a better word that the phrase Human Interface Device, which is the way your computer thinks of it.
The way it works is not all that different from a joystick. In some, a rubber ball inside rolls against the surface of your desk and turns rollers that send different electrical values (information about where the mouse is on your desk) to the computer. The computer then translates the position of the mouse and shows it as a cursor (usually) a pointy image on your monitor. This is not the best kind to get because, just like real mice, they leave a little bit behind. Every once in a while you have to clean bits of the rubber ball from the rollers inside.
An Optical Mouse uses an LED light and a light sensor to bounce LED light off the desk up to the sensor and that helps the computer decide where the mouse is. Some even use radio waves to send a signal without a wire to your computer. But then they don't look quite so much like a furry mouse because they have no "tail"!