You are talking about a Document Management System. Typically these systems allow users to save documents and delegate read/write access on a user or group level. They also allow for auditing of when users access documents. Some may also restrict editing and copying or even printing of a document (in addition to auditing all such actions).
There is simple to complicated. Some use a basic NAS with AD Group Policies. Others add a layer of encryption (Full Disk encryption, TrueCrypt, something else).
Finally you have the 'Enterprisey' systems. These have workflow and publishing management, complex ACLs and options on securing the documents and logging all activity.
Xeros sells a system called DocuShare (http://docushare.xerox.com/ though now marketed more as CMS) which I know several UN Organizations use. There is also KnowledgeTree (https://www.knowledgetree.com/)
These are just two of many. YMMV depending on actual business needs. Hope this helped.