suppose LOGO is not visible in this case priority is 
high ,but severity is low.....



suppose u have one login form in that form name field take 
255 character maximum,but after inserting 251 character 
application closes automatically in this case severity is 
high but priority is low . Like this we decide severity and 
priority.

Priority, 
          This assigned by the developer. Represents the 
importance of the bug. For eg. #1 priority bugs need to be 
fixed before the #2 priority bugs. #1 and #2 are the 
priorities that they assigned.     

Severity 
          Represents how bad is the bug. For eg. a bug that 
causes to crash the application are considered as the high 
severity bugs and need to fix them immediately.

Assigning severity and priority is as  below:

Any thing that is critical to business for instance if an
application is crashing or not responding.
EX: If you performed a search and the results are not
displayed at all or if the screen is frozen then consider as
severity one.

if the background color is supposed be white but its in red
then the severity is low.

Severity and priority are the two terms which shows the
bug/issue behavior. which is mention in the issue tracking
system.

Severity and priority is change as per the company standards.
In my company Severity and priority display as fallows. 

Severity :- Blocker,High,Medium,Low,Trivial.
Priority :- 5,4,3,4 and 1 ( '5' is highest priority )

I am trying to explain the how to assign the Severity and
priority of bug with the help of ATM software example.

1) Low Severity and Low priority bug.

a) Go to the ATM center and perform as fallows.
b) Login in the ATM with your password.
c) After successful login try to withdraw money with
   printed statement. 

 But machine withdraw money and not printed the statement.  
(So this bug assign as a Low Severity and Low priority bug.)

2) High Severity and Low priority bug.
 
a) Go to the ATM center and perform as fallows.
b) Login in the ATM with your password.
c) After successful login try to check balance and try to
withdraw money. 

But ATM machine not display balance and able to withdraw
money. (So this bug assign as a High Severity and Low
priority bug.)

3) Low Severity and High priority bug.

a) Go to the ATM center and perform as fallows.
b) Login in the ATM with your password.
c) After successful login try to check balance and try to
withdraw money. 

But ATM machine display balance and not able to withdraw
money. (So this bug assign as a Low Severity and High
priority bug.)

4) High Severity and High priority bug.

a) Go to the ATM center and perform as fallows.
b) Login in the ATM with your password.
c) After successful login try to check balance and try to
   withdraw money. 

But ATM machine get crash every time after successful login.
(So this bug assign as a High Severity and High priority bug.)

This way you can assign the Severity and priority to the bug.