DTC stands for Diagnostic Trouble Code. It may also be referred to as a fault code.
A DTC gets stored in the onboard diagnostic system of your vehicle. You can use an OBD-II scanner to retrieve these fault codes.
If a DTC is present in most cases it will cause the check engine light to come on and in some cases, the check engine light may flash.
Note that BMW uses DTC acronym for Dynamic Traction Control (DTC) which is a sub-function of the Dynamic Stability Control (DSC).