A Critical Issue, as the name says, is always critical and meant to be dealt with immediately. Critical Issues are those issues that are currently affecting the consumer. But declaring something critical can be very subjective, which is why only the Product Owner can declare an issue as critical.
As soon as it is declared critical, part of the team or a team member (depending on how much work needs to be done) should stop working on the current Sprint and focus on solving the critical issue.
If the issue is big enough, the Product Owner can take the decision to terminate the current Sprint to work on it instead. Read more on Sprint Termination here.