DCC Key Advantages: Instead of a traditional variable DC power pack being LIMITED to controlling the speed of just ONE locomotive, a DCC system sends many digital commands to control the speed of many locomotives using digital data encoded in the form of an AC track voltage. This eliminates the complicated layout "Block Wiring" normally needed to break the layout into electrical blocks to preserve the relationship between 1 DC throttle to 1 DC locomotive so control can be maintained. Instead the emphasis is placed on special circuitry in both the throttle and in the locomotive themselves to free you from the unrealistic "power management" actions, of throwing "block power" switches, needed to set up an "electrical route of track" for a given train. In other words, instead of you spending time "running the layout", DCC allows you to spend all your time "running your trains", or better yet, running multiple independent trains all at the same time.
DCC Key Technology: Advances in microelectronics allow specialized "micro-controllers" (miniature computers) called a decoder to be installed in each locomotive all the way down to Z scale. This same computer technology allows your throttle to remain small and light in your hand but yet control multiple trains. Together they expand the train control options way beyond what could ever be accomplished by DC. Specifically it also adds more FUN in the form of light and sound effects.
DCC System Parts: In a given DCC system, a Command Station is responsible for generating the DCC signal that contains the DCC commands to control any given decoder. A Booster takes that DCC signal and adds "power" to it to make it a usable to be able to power the rolling stock and engines. A Throttle (or Cab) takes your train commands (speed & direction + more) and passes them on to the command station. A Decoder listens and responds to DCC commands sent by the Command Station and controls the locomotive speed and direction independent of other devices on the track.
DCC System Packaging: On many simplest starter DCC systems, the Throttle, Command Station and Booster are often put together in the same box. On the other end, the highest power DCC systems tend to have separate boxes for everything. Except for low cost beginner or entry level DCC systems, most DCC systems DO NOT include a "power supply" to run the system. That must be purchased separately. Often a suitable power supply is offered by the DCC manufacture.
To learn more, I have several more detailed presentations about DCC that can be found at: NMRA DCC CLINICS