What exactly happens when you change the configuration settings in BIOS? Does it change some register value in the subsystem's register set directly?
Not directly, it just lets you configure the settings and stores them for further usage, so that when you later reboot or turn on the computer, the BIOS firmware configures the hardware based on the stored settings. So at that point, if it is such a setting that is set by writing it to chipset, it is written to the chipset. It may also be just some setting that selects if the BIOS does something or it does not, or how it does it.