Zettlr is happy with only a minimal installation (because it just needs the compiler), but if you want to fiddle around with LaTeX more you are free to also install the full package. LaTeX distributions come in two flavors: A 'full' installation featuring a host of graphical programs for writing TeX directly, and a 'minimal' installation that only contains the actual compilers.
LaTeX is a typesetting language that allows for a large amount of customization, but because it is a relatively large program, it does not come bundled with Zettlr. To export more advanced PDF files, you'll need to install LaTeX.
This will export a file to HTML and then 'print' it similar to how browsers print websites. Out of the box, Zettlr supports an export format called Simple PDF. There are two ways of exporting to PDF, however: Via Zettlr itself and with the help of an external program called LaTeX. Zettlr allows to export into a variety of file formats, including PDF.
