Clipping paths are a layer effect, which can be used to produce images in non-standard and custom shapes. A photo (or SVG object) can be put into (clipped) a triangular shape. Or any other shape you can imagine. The way it does this also reduces rendering speed and typing. Most browsers are able to render the commands correctly. I have tested Firefox and Safari successfully.
The top illustration of a typical Venn diagram is produced traditionally by creating 2 circles and offsetting by some amount. This is slightly more overhead. On a larger scale, or when using JavaScirpt, this may make a difference in rendering speed.
In the bottom diagram, we use a clipping path to produce 2 circles, which are slightly separated. However we only drew 1 circle, but referred to it twice with different attributes.
While both illustrations may look the same, the bottom one (using clipping) uses less resources, and allows for more control.
Let's see how this works ...