Priority - Priority is the order in which developer has to fix the bug.
Severity - Severity is how seroisly the bug is impacting the application.
Eg.
High Priority & High Severity: A show stopper error which occurs on the basic funcationality of the application . (Eg. A site maintaing the student details on saving record if it doesn't allow to save the record then this is high priority and high severity bug.)
High Priority & Low Severity: The spell mistakes that happens on the cover page or headin or title of an application.
High Severity & Low Priority: The application generates a show stopper or system error (for which there is no workaround) but on click of link which is rarely used by the end user.
Low Priority and Low Severity: Any cosmetic or spell issues which is with in a paragraph or in the report (Not on cover page heading title).