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Debian is a free operating system (OS) for your computer. An operating system is the set of basic programs and utilities that make your computer run. Debian uses the kernel Linux (the kernel is the core of an OS), but most of the basic OS tools come from the GNU project. Thus we refer to Debian as a Debian GNU/Linux operating system, giving credit to all its main originators. Debian GNU/Linux provides much more than just the OS---a wide range of application software is included too. It comes with a total of over 51000 packages, precompiled software bundled up in a nice format for easy installation on your machine.
Are you new to GNU/Linux? Finding where to start can be a daunting task! There are many places to start and there is so much information that it can be confusing. This wiki and the following web pages are very good places to start:
How to install Debian
Debian GNU/Linux Reference Card (PDF) - The 101 most important things when using Debian GNU/Linux