The high-level answer is that the NIC is designed as a PCIe device. It is physically connected to a PCIe hardware switch which communicates with PCIe endpoints like the i210 NIC you have.
When power is supplied to the system, the BIOS will scan for all PCIe devices on the system. The PCIe endpoints have built-in memory called PCIe config space which is configured and read by the operating system.
Once that information is properly configured, by either the BIOS or the OS, the OS and installed i210 drivers will be able to detect the i210 device ID listed in PCI config space and run the driver functions developed for the i210 adapter.