site links for DR purposes

when an organisation has a 'link' between 2 offices, e.g. a primary site with its core data centre, and a DR site whereby backups are written (or site resilience with 2nd infrastructure) to a DR site for disaster recovery etc, what actually constitutes that link, in terms of physical materials? And more importantly. kind of events/issues could break that link, leaving the primary site as a single point of failure, and what contingencies should organisations have in place for the event of the link breaking for whatever reason? I appreciate issues like earthquakes can damage physical infrastructure, but then smaller businesses only have so much budget for DR and 2nd sites etc etc.