I try to make it very simple.
Template engines in Drupal are software components that combine Data from Drupal with Templates from themes and show the result -which is final HTML- to the user.
+-----------+ +----------------+
| Data from | | Templates from |
| Drupal | | theme |
+-----------+ +----------------+
| |
v +--------+ v
+------| Theme |-------+
| Engine |
+--------+
|
v
+-------------+
| Final HTML |
+-------------+
Why Drupal uses theme engines? Because different developers have different coding tastes and Drupal does not want to deal with different template "coding styles" directly.
If you are learning Drupal theme design, you do not need to know theme engine design. Now a days, almost all Drupal themes use one engine: PHPTemplate which -in my opinion- is brilliant. You only need to know the theme engine API if you want to design advanced themes. For basic usage, even API knowledge is not a must.
For a simple start, try reviewing and tweaking a simple Drupal theme -like Bluemarine