"A person cannot gain something without losing something. To gain something, you need something of equal value. This is the Law of Conservation in Alchemy. At that time, we believed that was the truth of the world." - Alphonse Elric
Edward and Alphonse Elric are on a journey to find the Philosopher's Stone. A stone that can return Ed's right arm and left leg, and return Al's body. How did they lose these things in the first place?
They live in a world where the science of Alchemy is real and used on a daily basis. They committed the crime of a human transmutation trying to bring their mom back from the dead. Edward lost his left leg in the process, and Al lost his entire body. In an attempt to bring Al's soul back, Ed sacrificed his right arm to attach Al's soul to a nearby suit of armor. They start their journey with the definite thought of reclaiming that which was once theirs.