Snopes says that this information is bogus:
http://www.snopes.com/medical/homecure/eggwhite.asp
Further, the US Centers For Disease Control do NOT recommend this, because it is a potential source of infection.
Minor burns usually heal without further treatment. They may heal with pigment changes, meaning the healed area may be a different color from the surrounding skin. Watch for signs of infection, such as increased pain, redness, fever, swelling or oozing. If infection develops, seek medical help. Avoid re-injuring or tanning if the burns are less than a year old — doing so may cause more extensive pigmentation changes. Use sunscreen on the area for at least a year.
Caution
Don't use ice.
Putting ice directly on a burn can cause a person's body to become too cold and cause further damage to the wound.
Don't apply egg whites, butter or ointments to the burn. This could cause infection.
Don't break blisters. Broken blisters are more vulnerable to infection.
For more details read the entire text at these links, and please check out Internet sources before posting:
http://www.mayoclinic.org/first-aid/firs...t-20056649
http://msue.anr.msu.edu/news/fact_or_fic...oax_or_not