Music theory is complex by any standards and you’re not necessarily required to know everything, but there are some things you really should know. This is one.
In classical music, a fugue is a composition formally structured around a musical theme or series of notes. Fugues are characterized by frequent repetition of the theme, sometimes in modified form, by various voices in the composition. The word derives from the Latin fugere (to flee) and fugare (to chase), and that’s exactly the impression given by a fugal composition: a theme being chased by various voices in varying keys. The structure of a fugue is well-defined and based on deeper music theory, so it’s no small task to write a fugue and make it sound good at the same time. The fugue part of Bach’s Toccata and Fugue in D Minor (a “toccata” is another musical structure) is a great example. A short fugue is a fughetta, while a fugato is a small fugal passage in a larger non-fugal composition.
This has nothing to do with a “fugue state”, which is a reversible psychiatric disorder pertaining to amnesia.