Broken and De Saturated Colours

A desaturated colours are created when you mix a pure colour with black or white. You can say that a colour is broken when it's kind of grey and this is achieved when you mix a pure colour with it's complimentary. You can see this de saturated and broken colours everywhere, movies, posters, paintings, animations etc.
When you want to show a more sad or boring picture you use de saturated colours so it will give you that mood. You use the broken colours so it will get that desaturated mood.
Some times there is a combination of desaturated colours and a hint of saturation so it will give you a focal point and a more strong picture.