As paraphrased from the Nix Reference Manual:

A derivation is a specification for running an executable on precisely defined input files to repeatably produce output files at uniquely determined file system paths.

The derivation constructors defined in Typix extend this behavior by running typst compile/typst watch in a context where all the dependencies of your Typst project (fonts, images, etc.) will be made available to the Typst compiler, regardless of if they're already present on the system it runs on.