When you add a database connection under the Database Connections node in the Catalog tree in ArcGIS for Desktop, a file is created on the client computer that contains the connection information to a database that you provide. The default location for the file is \\<computer_name>\Users\<user_name>\AppData\Roaming\ESRI\Desktop<release#>\ArcCatalog, but you can move the connection to another location. For more information see http://resourcesbeta.arcgis.com/en/help/main/10.1/index.html#/Preparing_database_connection_files_to_share_with_other_users/00290000008v000000/.