A family of Microsoft relational database management systems designed for ease of use.
I had this problem message today when trying to open the database. In my case the error message "Your network access was interrupted. To continue close the database and then open it again." was completely wrong.
The error message should have indicated that the database was in use. I had at the time of attempting to open the database an Excel worksheet that had a link to it. Once I closed this Excel worksheet I was able to open the database in Access. This database is setup in such a way that it is not allowing concurrent use, even by the same user - but that is a separate issue.
The initial problem had nothing to do with Network access being "interrupted"... I am sure this error message as it currently stands is leading some people down the wrong troubleshooting path. No wonder there is so much agro about Access and this error message.