I don't really see the difference between the "repository" and "my files". They seem to have exactly the same functionalities
My Files is a unique area in Alfresco where you can create and store content, and no other Alfresco users can access it. So rather than saving content on your laptop or tablet, you can save it in Alfresco and still keep it private until it's ready to be shared.
You can access the My Files area from anywhere in Alfresco by clicking My Files at the top of the screen.Refer this Documentation
The Repository displays all the Alfresco Content Services content that you have access to, including content of all sites that you're a member of. Refer this Documentation