A subject repository is a repository of research outputs (and possibly metadata about such outputs) whose primary mission is to give end users access to all and only the research content available in a given subject.
For the purposes of this definition, a subject can be as vast as the mathematical sciences or as narrow as any dissertation topic.
Of course, some services we're inclined to label as subject repositories impose subject-independent constraints on their content (e.g. open access availability). That's why I inserted the "primary mission" qualification--this allows that some SRs have auxilarity requirements which impose some limitations on what content they aggregate.