The term is not defined in the general definitions section of the FAA's regulations. However, the FAA publishes a Pilot/Controller Glossary, available in the Aeronautical Information Manual (AIM) and on the FAA's Web site ( www.ama500.jccbi.gov/site/library/pcg/index.html ). The glossary exists primarily to promote a common understanding of the terms used in the air traffic control system. In this glossary, the FAA defines emergency as "a distress or an urgency condition." The FAA provides definitions for both terms. Distress is defined as "a condition of being threatened by serious and/or imminent danger and of requiring immediate assistance." And, urgency is defined as "a condition of being concerned about safety and of requiring timely but not immediate assistance; a potential distress condition." This is a good starting point to help you determine whether or not a specific situation is an emergency.
The FAA also provides some definition of what constitutes an emergency elsewhere in the AIM, which advises that pilots should not hesitate to declare an emergency when they are faced with distress conditions such as fire, mechanical failure, or structural damage.
It says that pilots should similarly not hesitate to declare an emergency when they are faced with an urgency condition that may not be immediately perilous but may be potentially catastrophic. The FAA further advises that an aircraft is in at least an urgency condition the moment the pilot "becomes doubtful about" position, fuel endurance, weather, or any other condition that could adversely affect flight safety. This is the time to ask for help. Don't wait until the situation has developed into a distress condition.
How do you request assistance in an emergency situation? Help is almost always available in the form of radio, radar, direction-finding stations, and other aircraft. If you are able to communicate, notify the facility you are currently monitoring or the controller you have been talking to if you are receiving flight following or are on an instrument flight plan. If you are not in contact with any local facility, you may want to use the radio frequency 121.5 MHz, which is constantly monitored. In addition, if you are unable to make radio contact and your aircraft is equipped with a radar beacon transponder, dial in the squawk code 7700, which is immediately recognized on a radar screen. The AIM recommends using the word "mayday" for a distress situation and the word "panpan" for an urgency condition, both of which are to be repeated three times when used. Practically speaking, the word "emergency" will also get somebody's attention to help you.
From a regulatory standpoint, do not be so concerned with these procedures that it takes your attention away from handling the aircraft. If you have lost communications, the fact that you cannot formally declare an emergency does not preclude reliance on the FAR 91.3 authority to deviate from the rules as necessary to deal with the emergency situation. Remember that the intention of the FAA's regulations and guidance is to give the pilot in command the responsibility to recognize such conditions and the authority to act in the interest of safety, even if it means breaking the rules.