Actually, a common use is to decorate the exception (add additional meta-data unavailable at the lower level where the exception occurred). This is often done by creating and throwing a new Exception whose parent is the original Exception.
Some systems such as Hibernate JPA catch JDBC-specific exceptions and normalize them to the standard JPA exceptions.
"privilege" comes from the Latin words for "private" and "law" (legal) and dates to feudal times. To "claim privilege" meant that you were above the laws that applied to the common people.