Sorry to join so late in the discussion
For me templates are:
1. Separation of HTML and PHP (subtly different than "presentation and logic", but nevermind that)
2. Higher-level and
short way of doing the most repetitive things:
- conditionals
- displaying arrays of data
- forms
Of course everything is possible with PHP alone, the point is that:
- it gets ugly (whether you mix HTML in the PHP or PHP in your templates)
- it needs more typing
- you keep writing the same boring patterns (how do you output an html table from a 2d array of data or a collection of database rows?)
I might add that some of the template engines out there (I'm looking at you, Smarty) do a lot of work, while still not solving these problems
I've already mentioned my template engine (still not GPL, sorry) , and it was in a very similar thread here some half year ago. There was a nice showdown of several engines so we could compare results and code. A yes, here it is (also started by Ninja

):
viewtopic.php?f=19&t=81806&st=0&sk=t&sd ... e&start=45
I have since had some more revelations about what more (and what less) it needs, just haven't had the opportunity for refactoring and features.