STM32F439 CDC driver, is using UART required?
The USB protocol can contain other protocols inside it.  CDC or Communication Device Class is one such protocol.  If both ends of the USB connection support CDC you can setup a serial communication between them.

For example, you can have an FTDI chip at one end of a USB cable and a Windows PC at the other.  The FTDI will convert serial RS232 data into a USB signal by first putting the RS232 data inside a CDC signal then putting that inside the USB signal.  At the PC end Windows will unwrap the USB signal then the CDC signal then make the RS232 data available on a virtual COM device within Windows.

A UART usually refers to a physical device (usually a constituent of an embedded processor) that can support RS232 protocol and perhaps a few other serial protocols.