There are two directions. Functional escalation goes to more expertise, from 1st level to 2nd or 3rd level or to the vendor. Hierarchical escalation informs management when an SLA is about to be breached, a major customer is affected or a decision is needed.
The quality of an escalation decides how fast things move. A good handover contains: affected systems and users, the exact error message, the time, what was already checked and with what result, relevant log excerpts, and a clear question for the next level.
A common problem is escalations without content ("doesn't work, please check"). They cost the next level the same diagnostic time all over again.