Photographs where the main subject and the background have a harmonious and pleasing colour scheme are much easier on the eye.  Unless you’re aiming for shock value the general rule is to avoid clashing colours.

For a basic understanding of how colours can work in harmony with each other just Google the phrase “colour wheel”.

There are certain established formulas for colour scheme harmony, including:

Monochromatic
Uses different shades and tones of a single colour, which can be accented with black, grey or white.  For example, an image primarily made up of shades of blue.

Analogous
Uses two or three colours that sit near to each other on the colour wheel, for example light greens and dark greens, or reds and oranges.  An analogous colour scheme can offer more interest than a monochromatic one.

Complementary
Uses colours that sit opposite each other on the colour wheel.  Classic examples are reds and greens or blues and yellows.  Think of how lovely golden Autumn leaves on a tree look when offset against a deep blue sky.

For the photographer, knowing how to combine certain colours can help to give ones images more interest and appeal.  A simple example might be to look at the primary colours in the model’s clothing, lingerie or makeup and choose a background that will work well with it and not clash with it.

Here’s a photo of Sophia in blue on blue (click to enlarge).