Before being able to explain the working mechanism of the integration one needs to describe the scenario it was developed for:
In the scenario there is already a TYPO3 website with different information and functionalities and there are already users registered for certain restricted contents. To access those contents they need to log in to that TYPO3 website using a login form.
The owner of the given TYPO3 website now wants to integrate e-commerce functionality to it. He wants to enable his registered users to additionally buy goods from his merchandise collection without sending them to another external web shop or letting them register again. He just wants them to use their given login information and sell items to them right within that TYPO3 website.
One could argue why the owner should not use TYPO3-internal shop extensions and certainly for some situations that would be a perfect solution. The answer is quite simple: Magento offers much more possibilities and a lot more flexibility on a higher level of source code quality and extensibility.
Additionally there were three main principles as a basis for the extensions: