Introduction into TypoScript
TypoScript is a configuration language used to configure both the frontend output and the backend of a a TYPO3 web site.
TypoScript is not a programming language but a means of configuring the website.
Frontend TypoScript
Frontend TypoScript is mainly used to configure which data should be send to the Fluid templates.
It can also be used to define settings send to Extbase plugins, metadata for a whole page etc.
In the beginning of TYPO3, TypoScript was used as templating language. In modern project it is not common to do that anymore.
For an introduction see Getting started: A quick introduction into TypoScript.
Backend TypoScript / TSconfig
Backend TypoScript, also called TSconfig, can be used to configure the output of certain forms etc in the TYPO3 backend.
Page TSconfig
Page TSconfig can be made available globally, on a per site or per page level.
For the possibilities see the Page TSconfig Reference.
User TSconfig
User TSconfig can be made available globally for certain user groups or certain users. It cannot be set for just one site or page. It can however override Page TSconfig.
For the possibilities see the User TSconfig reference.