Here we have our previous Venn diagram of 2 circles which intersect. We want to show the intersection as a separate color.
We can achieve this partially by making both circles less opaque, or more transparent, as in the top example.
However, depending on which circle is created first determines its position in the layer, and the color of the intersection. Without making use of blending techniques, this may have results that are not what we want, as seen in the top example. And as we add more circles (or other intersecting shapes), it gets messier.
By using a clipping operation, we can get what is required of the 2 intersecting circles, as in the bottom example. By doing it this way, we separate the intersection into a separate element, which can now be completely controlled as such (color, border, etc.).
We start with 1 circle in a <defs> element (definitions), so it can be referred to later in the 2 <use> lines. Note the x and y variables - they refer to the amount of offset (from the original circle) we want each circle to have.
If you're a programmer, the 'definitions' block is similar to references in Perl, or pointers in C. Or an alias or shortcut for the average user.
Next we set a <clipPath> that uses that circle.
Finally we put the <use> command in a <g> group block so the clipping operation can be applied to the group.
Still more ...