In my experience, I never use this attribute. However, in some cases it can be useful.
When you use Facelets, you can create templates or include pages inside another page. So you can imagine that a page could be included in several different pages. Take the example where the parent pages contain a form, with different id:
If you use prependId="false" (or on some components forceId="true"), the real ID will be simply foo, and then your code will be simpler as you will not have to care about the container of the input field.
However, you will have to use this attribute carefully, as you may get a duplicate ID error if you use thisprepend attribute too often...