From Joomla! Documentation
A template is a type of Joomla! extension that changes the way your site looks. There are two types of templates used by the Joomla! CMS: Front-end Templates and Back-end Templates. The Front-end Template controls the way your website is presented to the user viewing the website's content. The Back-end Template controls the way your website's administrative tasks are presented for controlling management functions by a Joomla! Administrator. These would include common tasks such as: user, menu, article, category, module, component, plugin and template management.
See also: Extension types (general definitions)
There are two types of templates used in a Joomla CMS powered website.
Front-end templates change the way your site looks to average users. Most of the templates you use or install will be Front-end Templates. Out of the box Joomla 3.x ships with two front-end templates, protostar (which is set as default), and Beez3. For simple sites these out of the box templates may be appropriate, but a majority of Joomla users will opt to install a third party template to suit the purpose of their site. A site can use multiple templates assigned to different menu items, but most beginners will just use a single template for their entire site.
Back-end Templates are much rarer than Frontend Templates. You will probably never need to change your Back-end Template. Back-end Templates allow you to change the way the administrator interface looks. Joomla 3.x ships with two back end templates, isis (which is set as default), and Hathor. The Hathor template was designed for accessibility, and may be appropriate for those with color blindness who require high contrast colors, or those using screen reader devices or keyboard navigation.
Joomla administrators should go to the page on Template Management for topics about managing your Joomla template or templates.
Joomla developers should go to the Template Development portal page for more topics on developing a Joomla template.