starting with ArcGIS 10.1 , the default connection to the geodatabase is (Direct Connection), which means directly connecting to the database without the need to connect to ArcSDE as an application server anymore (3-tier architecture). The ArcSDE libraries are already part of the ArcGIS Desktop software which means you can directly connect from Desktop the Enterprise Geodatabase (2-tier architecture).
I think this why ESRI are gradually shifting the name from ArcSDE Geodatabase, to Enterprise Geodatabase.
as you may know there are 3 types of Geodatabases provided by ESRI: File Geodatabase, Personal Geodatabase, and Enterprise Geodatabase.
To Create an ArcSDE Application Server Connection in ArcGIS Desktop 10.1:
1.in the search tool in ArcCatalog, search the word “ArcSDE“.
2.choose ‘Create ArcSDE Connection File (Data Management)(Tool)‘.
3.you will find a GUI interface that have different fields to be filled.
ArcSDE Connection File Location: is the file directory path on your local PC where ArcCatalog 10.1 SDE Connection Files are stored in.
ArcSDE Connection File Name: a name your propose for your geodatabase connection, usually ends with ‘.sde’ extension.
Server: is the server name where your Database is installed on.
Service: is your ArcSDE Application Server Port Number.
Username: is the Oracle Account name (already exists in your DBMS).
Password: password of your account.