Altmetrics measures scholarly impact on social media, i.e., how often research is tweeted, blogged about, downloaded, bookmarked or found in online reference managers such as Refworks, Zotero, Mendeley, etc. These measures are also sometimes called "usage statistics".
There are a number of tools that collect altmetrics, including the handily named "Altmetric".
PLoS Assessment of impact with Altmetrics is a service provided by the Public Library of Science (PLoS) in partnership with Altmetrics for all authors of works published in PLoS journals.
Web of Science search results provide usage counts of each article by users of the WOS database in the previous 180 days and since 2013.