Separation is quite an unwieldy topic to add to a 'basic composition' list but it really matters and will genuinely help you improve your images. There are a number of areas in an image where separation can apply, the most straightforward of which would be the separation of the topic from the background. This kind of separation is often easily achieved with the use of aperture to blur out the background effectively isolating the subject as is seen in this shot of a blue jay in alberta, canada.
The gallery below shows some more examples of separation being achieved through the use of aperture. A number of these images just wouldn't exist without that separation because they would have blended with their backgrounds to such an extent that the image would not be worth shooting, the images are actually created by separation.
You can also use light to bring separation and focus attention on your subjects as I did in the image below. These two children were watching the annual PRIDE Parade in Calgary Canada and had sat down in a bright sunny spot at their parents feet. The adults legs were mostly in shadow and I used a strong vignette to darken them further separating out my topic.
The gallery below shows more examples of separation by light and how it can help you create images across a variety of genres. Examples include nighttime, landscape, sunsets and portraits, separation by light is often one of the first things we notice about a shot because it forces us to look at the light first and pick out the intended area immediately before exploring the rest of the image.
Separation also applies to seemingly cluttered scenes such as the image below of a small park in Calgary Canada. The snow helps by giving a blank canvas along the ground and the coloured lights illuminating the trees pick them out beautifully before the lights of the city make the perfect background under a star speckled night sky.
Separation by colour is another useful way to bring out a shot. Obviously there is the 'selective colour' technique where black and white images leave one item in colour (usually a london phone box/bus or a new york taxi) but that got old very quickly and is rarely used now. But you can still separate using colour, as we saw earlier in the paragraph about aperture, this leaf shot uses both colour and aperture to to separate the topic from its background.
The gallery below shows how the use of colour to separate items within the image can bring excellent results. It's not just a matter of 'isolating' using colour as the image above does. It's about separation within the image as explained in the captions below.
I honestly feel that separation is one of the most important parts of the composition toolkit but as always, this one thing works far better in conjunction with the others. It's fair to say that this one (separation) like the 'rule of thirds' and 'framing' applies to virtually every shot you make.