An applet is an application that runs within a container - usually a web browser. Unlike Java applications, it is restricted in its ability to access local computer resources or make network connections unless it is digitally signed to indicate that it can be trusted. For more information consult any book on introductory Java.
"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.