A template set can be thought of as a "theme" or a "skin" for the site. You can switch between what template set (or even multiple template sets) are used just by "flipping a switch" in the admin panel. You can create one from scratch, start from the default ones that go with the software, or even upload a template set that a 3rd party designer creates for use with the Geo software. Once you create your template set, you can easily transfer it to other installations, or if you are a designer, can sell your custom templates.
For a more advanced explanation:
A template set is a sub-folder in the geo_templates/ folder. A template set can have file templates, media files1), and PHP files that store different aspects of the design, such as what template is attached to what page in the software2).
A template set can easily be backed up (just download it using the download button!) or restored (just upload the template set file using the upload button!). It can also be easily copied from one site to another3), and the design will be kept intact, with no changes needed in the admin panel besides "activating" the template set.
The templates are broken up into 5 main sub-folders, each for it's own type of files:
You can find more information on the tools that are available to use on template sets, in the documentation in this section of the WIKI.