A templating engine is a collection of scripts and files that serve to interpret the templating language and process the commands contained therein. As the data is produced from the database queries and from outside sources (if any), the template engine fulfills the function of plugging the data into a pre-determined format for display.
There exist a number of popular templating engines, each of which is designed to interpret different templating languages. Drupal is distributed with the PHPTemplate engine. PHPTemplate is popular for a variety of reasons, not the least of which is that the templating language it interprets is good old PHP—a preferred choice for many Web developers today.
Note
While PHPTemplate is distributed with the Drupal core, there are a variety of other templating engines that can also be installed and used with the Drupal system. Among the most popular are XTemplate, Smarty, and PHPTal. These alternative templating engines can be downloaded from http://drupal.org/project/Theme+engines.