What comes out
A GPX 1.1 file with every track point: latitude, longitude, elevation and time. That is what a map, a route planner, Google My Maps or a print needs. The file is named after the one you dropped in. What the FIT file held before conversion is in what is a FIT file.
What is left behind, and why
Heart rate, power, cadence and temperature. GPX 1.1 has no standard field for them; they live in the FIT file's record messages, and carrying them over would mean inventing a dialect other tools cannot read. If those numbers matter, keep the FIT — the editor reads FIT directly and prints the numbers from it.
Nothing is uploaded
The conversion runs in your browser. The file is not sent to a server, and nothing is stored when you close the tab. That matters more for a FIT than for most files: it starts at your front door and carries your heart rate.
Strava's archive
The bulk export from Strava is mostly .fit.gz files — the originals, compressed. Drop them as they are; each is unzipped and converted. If you only wanted one activity, Strava's Export GPX on the activity page is quicker — the export guide shows where it is.
The other direction
GPX to FIT — for loading a course onto a Garmin — is a different thing: Garmin Connect imports GPX directly and builds the course itself, so most people never need a FIT. If you want the file on the device without Connect, GPX to FIT writes a course file you can copy to the Courses folder.