The official definition of Conditional Tags, which can be found on WordPress Docs, is the following:
The Conditional Tags can be used in your Template files to change what content is displayed and how that content is displayed on a particular page depending on what conditions that page matches. For example, you might want to display a snippet of text above the series of posts, but only on the main page of your blog. With the is_home() Conditional Tag, that task is made easy.
WordPress Docs contain lots of informations on conditional tags and their employ; these are a must-read for every theme designer (at least a basic knowledge of php is required too).
On the web there are also some useful tips on creative usage of conditional tags. Here is a short list.
List of Conditional Tags on Wp.org;
The Ultimate Guide to WordPress Conditional Tags by Themelab;
How To: Use WordPress Conditional Tags to Hack Your Theme by WordPress Hacks;
About If Page Parent & Children Conditional Tags by Insitewebdesign.
Finally, there is an useful and popular plugin called Widget Logic, which makes use of Conditional Tags inside Widgets.