Priority 0. Look at this NOW. This priority should typically be tied together with an on-call rotation so that someone gets alerted. Services going down, significant parts of functionality going unavailable, major security problems—these sorts of things should result in a P0 bug. P0 bugs should be rare enough to warrant a formal review process around what caused the problem, its discovery, fixes applied, and lessons learned.
Priority 1. Fix within 24 hours. Examples include significant flaws in the product, bugs that affect a subset of the user base, bugs that impact the brand in a significant way.
Priority 2. Fix within a week. Minor problem, but it would be good to get fixed before then next major release of the feature goes out.
Priority 3. Fix within the next sprint (typically 2 weeks, but as long as a month).
Priority 4. Catchall priority for things that should go into the next sprint. Expect these bugs never to be looked at unless they get upgraded to P2s. Different teams prefer to have these lying around because they are a documentation of everything wrong or delete them because they are mostly useless.