a table with one column only? What is the use of a table with only one column? 

TableName
----------
Table_PK


Say I have a table named Academic and the staff has a positionID but this positionID is:

tablePosition
----------------
PositionID


thats it...only one column
My best and most speculative guesses are:

A lookup table. Used as a control/pick list for an application or report

A dimension.  Used in a data warehouse.

A log table. Used for logging.

Left over junk fron an adhoc query, data migration, report filter etc.

Aaron was right... But I couldn't resist ; )

To me, the names imply that it's to distinguish between academic and non academic staff. But unless you can test the application exhaustively in order to reverse engineer it you may never know the true/complete purpose for it.