OS Authentication means that the sql server client is passing along your credentials to the database. For SQL server that works nicely because it can use Microsoft active directory as credentials. Credentials are only half the picture though, that just means, I know who you are and I can be sure of it because you used a domain account authentication to log onto the windows workstation. The other half is authorizing the users in SQL Server to log on and provide them with permissions to see the data. You can authorize only some of the people in you active directory to log onto and read or write data in the database. You can give different permissions to people to different tables etc. So it is possible that you are logged into the workstation using your windows domain account and that account may not be authorized to log onto the SQL server instance.
