In an external doctorate, you are employed either by a non-university research institution (for instance a Max Planck Institute or a Helmholtz Center) or a company. Academic support is provided by TUM, which has the right to award the doctorate.
As a result, you will need a dissertation supervisor at TUM who can support your research project and your external doctorate. You will do your work and research mainly at the respective research institution or company, but you are also integrated into the academic environment at TUM.
An external doctorate at a company is often very hands-on, and lets you become part of the industry at an early stage. However, the strong focus on applicability also means you do not have the same level of academic freedom or academic depth as when performing basic research at a university. In addition, external doctoral candidates are less involved in the work of the department.