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.

Reference: http://docs.joomla.org/Glossary

The mechanism that offers users a stored view of (part of) a web page so that does not have to be pulled from the database. Joomla core offers three levels of caching:

Page caching
View caching
Module caching.

By default, Joomla does not cache any content. When caching is switched on, the stored views for this are stored in the filesystem for Joomla ../cache/page/ folder.