In Swarm terminology, a hive is simply a repository or collection of issues. The hive can live reside anywhere; on a website, in the source code repository for an application, on a networked filesystem, in a database, in a user's personal directory, etc.
A hive can be cloned, where every issue it contains is duplicated into a new hive. Additionally, individual issues contained in a hive can be branched and placed in a new hive. Clones and branches maintain a lineage back to their parent hives which allow for an exchange of information across multiple hives.