Regiments in the US military traditionally assign their companies alphabetical designations. Easy Company stands for the alphabetic letter "E", the phonetic designation of the fifth company in a battalion of any given Army regiment before the adoption of the NATO standard alphabet. Today, E Company would be Echo Company.
The series Band of Brothers follows Easy Co. of the 506th Parachute Infantry Regiment, United States Army 101st Airborne Division, from Easy's basic training at Toccoa, Georgia, through the American airborne landings in Normandy, Operation Market Garden, the Battle of Bastogne and on to the end of the war.
The title for the book and the series comes from a famous speech delivered by Henry V of England before the Battle of Agincourt in William Shakespeare's Henry V
"We few, we happy few,
we band of brothers;
For he that sheds his blood with me
Shall be my brother..."
Those who missed the first episode can read a recap on
TV.com or watch it on the EasyCo101airborn youtube channel
If you are interested in the real history, why don't you visit the official website of Easy Company?