The Marketing Cloud ID Service (MCID) provides a universal, persistent ID that identifies your visitors across all the solutions in the Marketing Cloud. It can replace ID generation code for services such as Analytics, Audience Manager, Target, and other Marketing Cloud solutions or features.
Previous to MCID, each Adobe solution identified the site visitor with a different ID. My favorite visual for this is the image below.
In the above image, we have an object. At the top of the screen, we have "IDs" for this object representing different languages. In reality, all of these IDs are identifying the same object. This is how Adobe's solutions worked prior to MCID with each solution identifying the same visitor with different IDs. With MCID deployed, each solution learns a universal language (English in the case of the diagram).
Having each of the solutions "speak" the same language, allows us to start sharing data and utilizing the most power pieces of each solution together. At Adobe, we call these Core Services or Integrations. Some of these are listed below: