Ex for high severity low priority: 

whenever 80% of module is released to the testing dept as 
far as the test engg is concerned the unavailabilty of 
functionality is treated to be high priority...but as they 
are under development the project lead will give least 
priority.

Ex for least severity and high priority:

upon customers visit all the look and feel defects are 
given high priority.

Ex for high severity low priority: 

whenever 80% of module is released to the testing dept as 
far as the test engg is concerned the unavailabilty of 
functionality is treated to be high severity...but as they 
are under development the project lead will give least 
priority.

Ex for least severity and high priority:

upon customers visit all the look and feel defects are 
given high priority.

when images are not updating in the application that is
low seviority ,high priority

High Severity and Low Priority:

Whenever we find the defects which have severe impact to 
the application (For Example: financial and safety impacted 
defects) and in the other hand we have sufficient time to 
fix it, then we assign the status High Severity and Low 
Priority.

Low Severity and High Priority:

If the defects have low impact to the application (for 
example: spelling mistakes in the fron page of the 
application) and we need to releas the product next day, we 
assign the status Low Severity and High Priority.

Hope it helps.