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.

for example:

ArcSDE Connection File Location: