"Components" are all the parts that attach to the frame and fork.
The quality of components has improved tremendously over the years. If you are buying a "previously-loved" bike, it might be a good idea to upgrade its components over time.
Besides locomotion, bicycles have to perform a host of other functions (braking, shifting, etc.).
What approach to these functions works best for you depends on fit (your proportions), and ergonomics (what mechanism feels/works best for you).
There is a mind-boggling number of after-market parts available for every single part of the bicycle.
No fenders? Polycarbonate? Hammered steel? Bentwood?
The choice is yours ...