A pilot who is fatigued has poorer attention, concentration, coordination, and is less able to communicate or make sound decisions. Fatigue is described as being acute or chronic.
Acute Fatigue
Acute fatigue is short term. It results from a short period of stress or excitement, or simply a bad night's sleep. Because acute fatigue is short term in nature, it's solution is one night of good rest.
Chronic Fatigue
Chronic fatigue is long term, resulting from ongoing stress, poor diet, disease, or lack of sleep over a long period of time. Chronic fatigue has more serious health consequences and requires treatment.
The Danger of Fatigue
Whether the fatigue is chronic or acute, it is very dangerous when mixed with flying. A pilot who is about to begin a flight will be more physically and mentally active during the preflight activities. The pilot might not feel tired during the taxi and takeoff, as a result of that recent physical activity and the higher workload of the taxi and takeoff. However, during cruise the workload is at a minimum, and the pilot is sedentary. It is at this point that the highest workload of the flight is encountered, the approach and landing. Situational awareness, critical to good decision making, can be severely reduced by fatigue. In extreme cases, the pilot might even accidentally fall asleep.
Even on flights of short duration, perhaps with little or no time spent in cruise flight, fatigue is dangerous. A fatigued pilot might not feel tired, due to the continuous workload and desire to stay alert. However, the ability to think clearly, make sound decisions, and generally operate safely are significantly impacted.
Avoiding Fatigue
Avoiding fatigue is as simple as getting a good nights rest and not flying too much in one day. Being properly rested is so tied with flight safety that the FAA has created regulations that govern rest and duty periods for many types of operations. For example, a flight instructor is not allowed to fly more than eight hours per day. Flight crews are required by law to get a good night's sleep. They are even required to take at least one day off each week. The existence of these regulations illustrates the importance of being properly rested.
It is not practical to attempt to mandate a private pilot be properly rested. However, the private pilot is still responsible for safety of each flight. Beginning or continuing a flight while fatigued is an unsafe decision. Similar to driving, its a smarter idea to get a hotel and not make it home, rather than accept the danger of pressing on while tired.