What is the difference between severity and priority?

Here are the main differences between severity and priority:

Severity	Priority
In simple words, severity depends on the harshness of the bug.	In simple words, priority depends on the urgency with which the bug needs to be fixed.
It is an internal characteristic of the particular bug. Examples of High severity bugs include the application fails to start, the application crashes or causes data loss to the user.	It is an external (that is based on someone's judgment) characteristic of the bug.  Examples of high priority bugs are the application does not allow any user to log in, a particular functionality is not working or the client logo is incorrect. As you can see in the above example, a high priority bug can have a high severity, a medium severity or a low severity.
Its value is based more on the needs of the end-users.	Its value is based more on the needs of the business.
Its value takes only the particular bug into account. For example, the bug may be in an obscure area of the application but still have a high severity.	Its value depends on a number of factors (e.g. the likelihood of the bug occurring, the severity of the bug and the priorities of other open bugs).
Its value is (usually) set by the bug reporter.	Its value is initially set up by the bug reporter. However, the value can be changed by someone else (e.g. the management or developer) based on their discretion.
Its value is objective and therefore less likely to change.	Its value is subjective (based on judgment). The value can change over a period of time depending on the change in the project situation.
A high severity bug may be marked for a fix immediately or later.	A high priority bug is marked for a fix immediately.
The team usually needs only a handful of values (e.g. Showstopper, High, Medium and Low) to specify severity.	In practice, new values may be designed (typically by the management) on a fairly constant basis. This may happen if there are too many high priority defects. Instead of a single High value, new values may be designed such as Fix by the end of the day, Fix in next build and Fix in the next release.

I hope that you are now clear about the difference between severity and priority and can explain the difference to anyone with ease.