Severity: Impact of the defect on the Application. Assigned 
by Testers.

Priority:Impact of the defect w.r.t users. 
        : How fast we have to solve the defect.

Severity is seriousness of the bug
where 
Priority is How fast the bug should be rectified?

severity describes seriousness of the defect with respect 
to functionality
where 
priority describes importance of defect to solve with 
respect to customer.

Severit: how bad the defect and its reflect or imapact on 
the s/w application with respect to the customer 
requirement and on the user.severity given by the test 
engineer.

Priority: How important the bug when it is to fix.It 
shopuld be fixed on the basis of importancy of requirement.
Priority of the defect decide by the Developement team 
member.

hai
 
Severity -  impact of the bug on the functionally 
priority - order of important of the bug

I can differenciate with example
suppose we identify two bugs
1. The client logo is not appearing on the web site but the
site is working fine... in this case the severity is low but
the priority is high because from company's reputation it is
most imp to resolve. After all the reputation wins more
clients and projects and hence increases revinue 

2. The Qaurterly statement event is not triggering from the
website and we are just at the begining of the new quarter
after a new release. 
In this case the Severity is High but priority cauld be low
becase we have time till the quarter ends to fix the bug

So the botemline is that in the priority v/s severity 
matrix the priority is completely bussiness impact driven
and the severity is completely technical impact driven. :)

Hope this helps !!

severity means how severe it is effecting the functionality

Priority means how fast it has to be fixed.

the diff will be more clear if u go for an example of Low
priority high severity  and high priority low severity 
1. low p high s :- suppose we have a link on our site that
is visited very rarely may be in once 1000 times on which
our system crashed that is High Severe because whole system
crashes but Low priority because Link is very rare.....
2. misspelled company name or missing logo from front page
have no impact on s/w functionality but having a worst
impact on company's goodwill so this is this case of high
Priority but Low severity........
 i hope u will understand...

Severity:Severity indicates the criticality of the
failure[Functional or procedure failure of the complete
system with no work around, or defects that are urgent
customer care driver].

Priority: The order in which the defect should be fixed.

Severity is in terms of application under test where as
priority is in terms of customer requirements..