What is Fluid?
Fluid is a templating engine which lets you display content on a website very easily. A specific file (the template) is pre-processed and the placeholders within will be replaced with the required dynamic content. This is the basic concept of template engines - the basic concept of Fluid is the same, however dig a little deeper and Fluid reveals itself to be far more powerful than any other PHP based templating language available.
Fluid's power lies within so-called ViewHelpers, little helpers to extend the original functionality of templating to make the life of HTML coders easier. Fluid is completely XML-compatible, allowing to use the power of IDEs to auto-complete and validate your templates.
Fluid was initially developed for the FLOW project starting in 2008 and then integrated into the TYPO3 Core shortly afterwards. Since 2016, it is a complete standalone PHP library which can be included in any PHP software project via composer. Find the source code available on GitHub.
TYPO3 uses the standalone library since version 8, and contains an adapter that contains some TYPO3-specific ViewHelpers.
How do I start?
Have a look at the documentation of the Fluid Standalone package on GitHub. or get a comprehensive introduction to Fluid in the context of "Developing TYPO3 CMS Extensions with Extbase and Fluid" or have some Cheat Sheets at hand for your reference.