When you make some changes to something, you have created a new "version" of it. For example, if you draw 5 pictures of the same person at around the same time, each picture that you drew was a "version" of that drawing.

In the case of software, companies add new features and fix problems with their software. They release these changes to their customers as a new "version". The new version usually has a new name or a number (like "Microsoft Word 2007", "Adobe Photoshop CS4", etc.).