How is a single color represented in a digital image?

A single colour is represented in a digital photo by the many tiny pixels in the photo. Those pixels are actually individual squares holding their own single colour.

Computers represent everything as numbers.they represent everything using only two numbers, zero and one.
There are many ways to represent colors with numbers. The most common method in computers is to represent the amount of red, green, and blue primary lights required to mix together to create the desired colors.
This is  because most computer displays work by adding together amounts of RGB primaries and the numbers can be used to directly display colors.