A palmtop computer is a personal computer or other electronic device that has many of the same features as a computer and fits in the palm of your hand. A good example of an early palmtop computer is the PalmPilot as shown in the picture. Because of their size early palmtop computers did not have a keyboard or a mouse and often relied off a pen that used Graffiti or something similar.
The term "palmtop computer" was an early term used when computers were big and cumbersome and small cell phones and even smartphones were not yet invented. Today, this term is rarely used to describe a computer that fits in your hand because of the invention of the Smartphone.