I am asked the question in the title all the time, and the answer is actually pretty simple...
When building an application that integrates with Eloqua, the choice of where to host it is entirely up to you, but it must be somewhere external to Eloqua.
After I give that answer, the next question usually involves, "then what is cloudconnectors.eloqua.com? Isn't that where Eloqua hosts the app for us?"
In order to clarify things, let me answer those two questions...
What is cloudconnectors.eloqua.com?
Quite simply, this is the site where the Eloqua labs team hosts apps that were developed in-house. It resides outside of Eloqua, and a separate login is required to access apps on the site.
Isn't that where Eloqua hosts the app for us?
The answer here is no, Eloqua does not host externally developed apps.