Colour relationships are how colours relate to one another and the influence they have on one another. When two contrasting colours are put next to one another the colours jump out at you, this can make for striking artwork.
To understand how colour works I recommend studying the colour wheel and sticking one into your sketchpad for reference. The colours that are opposite on the colour wheel are know as contrasting colours, these are the colours that have the most impact when placed next to one another for example red and green.
How can I learn about Colour Relationships?
Try playing with colour by placing colours together in boxes (see below) you will notice how some colours stand out next to others.
The colours next to one another on the colour wheel (red, orange, yellow) are known as harmonious and they will blend into one another. Once colours are understood you can start using them to create mood, make your artwork really vibrant and give your work ‘feeling’ like warmth, happiness, stillness, distance etc.
Try painting in just two or three colours and see the difference. It is interesting to do a few studies like this, it will teach you about colour and colour relationships.
See my post How can I learn about Colour? for more advice.