If you don't specify anything here, the transition on the related issue will be performed under as the same user , who triggered this post function on the origin issue. Thus Therefore that user must have the necessary permissions on the related issue.
However, in In some restrictive setup setups, that user might not be allowed to do so have the permissions on the related issue . He or even might not even see have access to the project of the related issue!.
With 'Perform As User' you can specify a different user account which that owns the necessary permissions. Usually, this user account is assumed to be only technical (impersonation), with broad permissions, but not used to log into Jira by in life personsa Jira account as a person.
In combination with the 'User is in Any Users' Condition, you can hide a transition from all other users than the 'Perform As User' user. For further example go here.