In the most literal sense to digitize something means to turn it into digits or numbers. In a more practical sense it means turning something into the electronic language a computer can understand.
The opposite of digital is analog. A good example of an analog device is a wristwatch with hands which move continuously around the face. Such a watch is capable of indicating every possible time of day. In contrast, a digital clock is capable of representing a limited number of times (every tenth of a second, for example).
Humans experience an analog world. Vision is an analog experience, because we see infinitely smooth gradations of shapes and colors. However most analog events, can be simulated digitally. For instance, photographs in newspapers consist of an array of dots that are either black or white, a classic digital format. From a distance, the viewer does not see the dots, but only lines and shading, which appear to be continuous. Although digital representations are approximations of analog events, they are extremely useful because they are easy to store, transmit and manipulate electronically.
This is the principle behind a digital image. The image itself exists in an analog form, as visible light waves in the air. These light waves are captured and translated into a digital form, that is numbers which represent an approximation of the image similar to the dots in a newspaper photo. When you view the image, the computer reads the digital data, sends it to the monitor which displays the digital image as a series of pixels or colored dots. You view the image and your brain converts it back to a continuous analog image.
The more dots, or digital bits, used to simulate the image the higher the resolution. A four megapixel camera uses four million dots per image while an eight megapixel cameras uses twice as many.