The actual implementation is a secret of the vendor of the converter.
It works like this. Upon receiving, the serial stream of bits is sampled by the UART of the converter to a stream of bytes. The bytes are then send to the PC via USB packets. The OS driver then makes the bytes available to the receiving process via the COM API (Windows) or device files (Linux, ...).
The other way round, the process writes bytes to the COM API or device file. These bytes are then send to the converter via USB packets. After that, the UART converts the stream of bytes to a serial bit stream which is then outputted.
Basics of the USB protocol can be found in the USB Standard documents or in a tutorial on the internet.