It may sound simple, but writing a definition of what constitutes an emergency can become a political battle. It may be part of a larger SLA document, or a stand-alone policy written to help helpdesk personnel make the right decision. This definition is often included in an escalation policy.
Often, we find that SAs are overloaded because every customer claims to have an emergency that requires immediate attention. SAs who feel that customers are using this claim to boss them around lessens morale and increases stress levels. Having a written policy empowers SAs to know when to push back and gives them something physical to point to when they need it. If the customer still disagrees with this assessment, the SA can pass the issue up to someone in management who can make the decision. This lets the SA focus on technical duties and lets management focus on setting priorities and providing resources.
Every company should be able to define what constitutes an emergency. At a factory, an emergency is anything that stops the assembly line. At a web-based service or ISP, an emergency might be anything that will prevent the service from meeting an SLA. A sales organization might define an emergency as anything that will prevent a demo from happening, end-of-quarter revenues from being booked, or commissions from being processed. At a teaching institution, which has tightly scheduled lecture times that cannot be simply moved or delayed owing to a system outage, an emergency might be anything that would disrupt scheduled technology-dependent lectures, as well as other matters related to the seasons of the school year: new-student arrival, exam deadlines, grade publication, graduation, new-student recruitment deadlines, and so on.