How does USB-C handle simultaneous data and video?
This mode is actually called DP-ALT mode, DisplayPort Alternate mode. USB 3.0/1/2 cable has four high-speed differential pairs. In normal USB operations only two pairs are used, the other two are just hanging unused. In DP-ALT mode the host system has a mux that connects two DP lanes into two unused pairs on USB Type-C connector. More details can be found in this early article from anandtech, and here is an illustration of the idea how it is usually implemented:



There are several modes for DP+USB, with 2-lane DP variant, and also a 4-lane DP with USB over AUX lines, or USB-2.0 only over regular D+/D- wires.

To get into this mode, both provider and consumer must negotioate over CC lines using PD messaging system.