What is the use of this pin in my AC to AC converter
That looks like the center pin of a standard DC Power Jack (also known as a barrel jack).

Edit: Note that this is just the name of the type of connector, so if your adapter is an AC to AC adapter, it still supplies AC.

The inside of the jack makes contact with the outer contact on the plug, while the pin makes contact with the inside of the plug.

DC Jack:



DC Plug:



They are available in different sizes and diameters. There are lots of related questions you might find useful:


How can I tell the size of a barrel power connector?
Connecting a DC barrel jack to a PCB board
What to do with third contact in DC barrel plug with only two input contacts
How to solder wires on to this power barrel plug?
Electrical part question (about DC power jacks)