We recommend all users uninstall Flash to ensure their systems are secure, because Adobe will no longer issue security patches for the software. It has provided instructions for removing Flash on Mac and Windows PCs.
Webmasters should be on the lookout for content on their sites (most likely embedded material produced by third parties) that stops working after 12 January.
Further information is available on Adobe's website.
The BBC's article on the news includes a brief history of Adobe Flash and its role in the development of website content.