The main reason people use template systems is to separate logic from presentation. There are several benefits that come from that.
Firstly, you can hand off a template to a web designer who can move things around as they see fit, without them having to worry about keeping the flow of the code. They don't need to understand PHP, just to know to leave the special tags alone. They may have to learn a few simple semantics for a few tags but that is a lot simpler than learning the whole language.
Also, by splitting the page into separate files, both programmer and designer can work on the same 'page' at once, checking in to source control as they need, without conflicts. Designers can test their template visuals against a stable version of the code while the programmer is making other, potentially breaking changes, against their own copy. But if these people were both editing the same file and had to merge in different changes, you can encounter problems.
It also enforces good programming practice in keeping business logic away from presentation logic. If you put your business logic mixed in with the presentation then you have a more difficult time extracting it if you need to present it differently later. Different modes of presentation in web apps are increasingly popular these days: RSS/ATOM feeds, JSON or AJAX responses, WML for handheld devices, etc. With a template system these can often be done entirely with a template and no or little change to anything else.
Not everybody will need or appreciate these benefits however. PHP's advantage over Java/Python/Ruby/etc is that you can quickly hack up web pages with some logic in them, and that's all well and good.
