What this is basically saying is that anything relating to the final output should be determined in the template, while any data handling or processing should be done in your PHP files and classes. There's a little more to it than though, which we'll soon see.
They introduce the reader to what the two sides are (application and template logic) and an example of the "bad way" to do things - application logic in your presentation layer. To counter this, they give examples of proper structure with examples like checking strings, alternating background colors, showing a counter, and the inclusion of another template.
A few other suggestions are made as to the good and the bad of templating your site, including two cases showing both sides.