Free practice is a widely used term in motorsports, but I specifically wonder what "free" means in Formula 1. I've some choices without any reference.
Is it related to drivers, car parts, number of laps, or something else?
There is no official reason why the term "free" is used to describe practice sessions, but here are a few reasons why the term could be used:
Attending a free practice session is not mandatory, the drivers have to take part in at least one practice session to be allowed to start race. Here is the regulation from the Official Formula 1 sporting regulations:
31.1 No driver may start in the race without taking part in at least one practice session.
However teams want to obviously run as much as possible during those practice sessions as it gives them the opportunity to setup the car for the race weekend and better understand the tyres (how they react in the current conditions and which tyre strategy will be optimal during the race). Track characteristics and track conditions (e.g. air temperature, track temperature, humidity, if the track was recently resurfaces or not, ...) vary between each race, so the car needs to be set up differently every time and the right tyres need to be chosen. Those free practice sessions give the teams the chance to do so.
They obviously rely a lot on all the data that they have gathered from other races, from testing sessions, from their windtunnel runs and CFD cases, but the data that they gather during the free practice sessions will define the setup they will run in the qualifying sessions and the race.
Free practice – During these practice sessions before a Grand Prix, the lap times are recorded, but they have no influence on the starting order or the result.
The only sessions that have an impact on the final results are the Qualifying sessions to determine the grid order and obviously the race.
In a nutshell, it's called "free" practice session because the sessions aren't mandatory and the recorded lap times have no influence on the race weekend.