What voltage does a laptop provide over USB C?
I would only really like to understand the actual theory behind how
  the profiles work.


The actual "theory" is changing every year or so. So it is impossible to understand.

The fixed power profiles are from PD Rev. 2.0, which is superseded by PD 3.0 specifications. In PD 3.0 there is an option to have variable voltage profiles.

The limitation of "19.5V" in laptops is not something of major concern, since laptops are not meant to be a major source (provider) of power. The higher power profiles are envisioned as a feature for main universal AC-DC PSU that can feed a chain of devices without a need for additional AC-DC adapters. If a particular laptop can't handle 20V input, than it won't be offering this profile downwards, that's it, although step-up DC-DC converters are not something unheard of, if somebody wants to make a really crazy laptop.

The full PD specifications can be found as a part of total USB 3.x zip file from USB.ORG site.