On the left of the ArcCatalog window, you see the Catalog tree. One of the folders in the Catalog tree is called Database Servers. Double-click the Database Servers folder to open it.

To disconnect from a database server, right-click the database server and click Disconnect. When you are not connected to a database server, there will be a red X on the database server icon.

To reconnect to the database server, either double-click it or right-click it and click Connect. When the connection is established, the red X will disappear from the database server icon.