Software can be Free both in terms of cost (free as in beer), and liberty or freedom (free as in speech). For a detailed description, please see the Wiki entry for Free Software.
Free software is available for all platforms and operating systems, and there are even free operating systems themselves. If you are used to Microsoft Windows (for example), you don't have to switch to a free OS in order to use free software. Here are some examples of very well known applications:
Probably the best known and widely used free software. This is a web browser which is certainly the functional equivalent of Microsoft Internet Explorer (or IE).
An office suite which can replace Microsoft Office for most users. MS Office does have more features, of which the vast majority of users do not use - or even know about.
The GIMP is the GNU Image Manipulation Program. Suitable for tasks such as photo retouching, image composition and image authoring. It works on multiple operating systems, and in many different languages.
There are thousands more examples of great free and open software - too many to list here. Here is a site dedicated to finding Open Source Alternatives to well known commercial or proprietary software.