High severity and high priority:
suppose an applicaton crush after start.

High severity and low priority.
In start up window application name or spelling is wrong.

Low severity and high priority.
suppose a database needs to be updated monthly but it gives 
error.


Low severity and low priority
A scrolling button is there at the frontscreen.

H-P H-S  –   Login id & Password Encryption is not done at 
client Side
H-P L-S  –  Company Logo is mismatch
L-P H-S - Session is not expiring after clicking on logout 
button in 
any screen.
L-P L-S   -  Client Side Validation for text box & Field

High severity and high priority.
application crash

High severity and low priority.
spelling mistake on homepage 
e.g missing h in yahoo.com

Low severity and high priority.
Session is not expiring after clicking on logout 
button in 
Low severity and low priority
spelling mistake not on homepage

Hi everybody what I found is there is a little clarification
needed for simple concept of severity and priority.severity
shows the impact on the application which can be high or low
like system crash will have high severity.while priority
denotes how much it is important to fix the bug.so if system
crashes once in say 150 times then it will have low priority.

so examples for these are below:-

1.High severity & low priority :- If a application crashes
on very rare occasions and changes are very low of
crashing.so severity will be high but priority will be low.

2.High severity & high priority:- if a application crashes
very frequently and duly visible or first time the
application came from development team to the testing
department.

3.Low severity & low priority:- it is merely just a
enhancement bug which the client wishes like changing the
background colour of user interface,also like adding a
button like 'back' to navigate previous page.

4.Low severity & high priority:- In this case if the name of
the company on its home page is misspelt will be considered.

So to find that in which category the bug comes always
remember one thing that Low severity bugs are mostly related
to GUIs and high severity bugs always related to things like
system crash.severity is always technical while priority is
for business purpose.