It just means the part (piece, component, subset...) of a larger set of regulations.
If you go to the USA, the aviation stuff (known as FARs or Federal Aviation Regulations) are actually a subset of federal regulations known as "14 CFR - or 14th Code of Federal Regulations".
So an airliner is certified in the USA to "14CFR part 25", also known as "FAR-25".
In Europe, the same aircraft would be certified to a similar document called CS.25 "Certification Specification No.25", unless it's an older aeroplane in which case it's JAR-25, "Joint Aviation Requirements, part 25".
As a convenient international shorthand, we all call those regulations collectively "Part 25". There's a similar set for light aeroplanes we call part 23, light helicopters are part 27, large helicopters are part 29. Regulations for aircraft maintenance are in part 145, licenced engineer qualification in part 66.
That shorthand has just spread to all other parallel regulations. And so the regulations to do with flight crew licencing are being referred to as "Part FCL", as a convenient shorthand that (almost) everybody understands.
There are loads of others - part M is to do with maintenance, part E is to do with engine certification....
So, it's just a word, and doesn't stand for anything.
G