The term “theme” when used in the context of content management systems (cms), galleries, or e-commerce systems refers to the use of templating systems such as (phptemplate or smarty) which are used to structure and control the appearance of dynamically generated web content. This sounds complicated, and in reality it can be very complicated, a simple way of saying it is that a theme controls the appearance of dynamic websites while leaving the majority of the site functionality untouched. This important in so that there is a clear separation between the information that makes up the content of a site, the programming that allows the site to do interesting tricks, and the way your site looks. This way if you decide to change the way your site looks in a year or so, you are not forced to change anything but the theme (hopefully).
Drupal by default uses the phptemplate system, though it provides support for other templating engines. I’ve used other templating systems and I can say without hesitation that Drupal’s is the most flexible and easy to use.
Drupal ships with several default themes out of the box, but most people who are interested in building a serious website aren’t even going to consider using these themes due to the fact that it would make their site look like a cookie cutter copy of thousands of other sites. There are also a number of contributed themes that are available to be downloaded. Some of these themes are decent, but again most professional websites won’t tend to use a contributed theme either. One exception to this I find is the RootCandy theme, which is an excellent theme for the administration sections of drupal sites. This theme is used on a large number of production websites, though never visible to the general public.
In the end, most professional websites that are built with Drupal make use of custom Drupal themes created specifically for their needs. With a well done custom theme it can be virtually impossible to discern that your site is built with Drupal. It should be noted that “can” is highly dependent on the skill level of the themer and the requirements of the project (Some people aren’t interested in hiding all signs of Drupal).