When another outlet republishes or otherwise distributes your content, knowing this is happening and analyzing the resulting engagement helps you and your funders understand your reach and how you are fulfilling your mission.
INN Labs offers members a Republication Tracker Tool. It allows publishers to share their stories via other websites and then track engagement of those shared stories with Google Analytics.
Simple metrics include page views and total unique users. Sites offering paid subscriptions or asking users to contribute or become members measure those “conversions” similar to how an e-commerce site tracks sales. Publishers are increasingly using time on site, time spent with particular content and frequency of visits to measure engagement.
Ample background on metrics is available online, including this article from Mediashift.org.