Open Source Software (OSS) is software whose source code is openly published, often developed by voluntary efforts and usually available at no charge and released with a licence defined by the Open Source Initiative. The licensing is intended to promote the sharing of code and prevents it from being redistributed under a more restrictive terms. If you distribute or sell any code based on open source software, you have to make the source code available to your customers.
Without OSS, the Internet would not exist today. In fact OSS drives 60% of all websites, including some of the busiest in the world, and is growing rapidly in the corporate world. Webservers such as Apache, operating systems such as all versions of Linux and BSD, scripting languages such as PHP, PERL and Python, databases such as mySql and PostgreSQL and applications such as Firefox and Open Office are all open source software. All of these products are best of breed and are mission critical in some environments.
These products then lead to the next tier of Open Source software which provide targeted business solutions. Content Management Systems such as Mambo or Drupal, Customer Relationship Managers and sales prospecting tools such as SugarCRM provide highly specialised yet configurable and flexible tools to meet business requirements throughout the world.
The core business case for open-source is high reliability and accessibilty. OSS is peer-reviewed software and demonstrates a reliability that closed proprietary software envies. Mature open-source code is as bulletproof as software ever gets. If problems are discovered, they are fixed immediately and you don't spend your time reinventing the wheel.
Finally, if the software doesn't provide all the functionality you require, you can use OSS as a starting point and add features as you require them. That is why there are so many Linux distributions and many other projects germinate from the seeds of other similar projects. SourceForge and Freshmeat are repositories where software can be discovered (see the sublink on the left).