Each pixel has its own 'value', which comprises of a number of binary digits - 0s and 1s. The following illustrates a very simple example of this. Please note, these values have been made up, so they probably aren't correct for the colours!
In this example 8 bits have been assigned to each pixel.
Each pixel can be edited individually, however this is very time consuming. Generally you edit groups of pixels. You would only edit individual pixels if there were flaws in a photo, eg removing spots from celebrities' faces.
As you can see, unlike vector graphics, pixels aren't good for sharp edges due to their square shape. A technique called Anti-aliasing can be applied to smooth the sharp edges.