I am embarrassed to say that only somewhat recently did I figure out truly what a layout-based presentation (a.k.a. two-phase render) was all about. I’ve even used them before, and didn’t know why.
If you can’t tell someone clearly what is the benefit of two-phase render, go and read the Smarty documentation on it right now. Smarty calls it template inheritance, but IMO template inheritance, layouts, and two-phase render are all the same pattern.