What is the relationship between the repositories that is accessed using /obr and /repository in Apache ACE??
There is no strict relationships between these.
/repositorycontains all ACE's metadata about deployment, i.e., states which artifact should go where, in which an artifact is represented as a URL.
/obr/contains ACE's own implementation of an OBR. It is packaged as separate bundles, and ACE can be deployed with or without it.
To provision, ACE doesn't need an OBR. However, the Web UI assumes an OBR is available for uploading artifacts to, so they can be provisioned. The ACE OBR extends the specification, in that is allows non-bundle artifacts to be uploaded.