IMHO, putting both Priority and Severity is just bureaucracy.
In practice, you just need one measure of "importance". Often, priority is used for it, and severity is then used as technical term like "high = crashes system or makes it unusable", "medium = buggy behavior, potentially harmful", "low = nuisance, annoying but harmless"
Usually, priority goes hand in hand with severity. A few counter examples are a "nuisance where everyone always complains" or a "crash having occured once in an exotic environment".
...but, in the end, as a developer (or manager, etc) you only need to know in what order you should fix/improve things, that's all. So one measure is enough.
The need of priority is clear: it's to know in what order the bug reports should be tackled. The other one, IMHO as usual, is bureaucracy. Why do you need it? It's apparently useless for sorting because priority does that. And the consequences (severity description) is described in the bug report anyway.
I even think it is harmful because it makes it less clear what bug is more important:
- Some may think a "critical" bug has higher priority than a "high-priority" bug.
- Some users reporting a bug may confuse severity and priority
- ...altogether, it rather adds confusion as to what order the bugs should be tackled