Full Metal Alchemist: Brotherhood is basically a remastered version of Full Metal Alchemist, and this remastered anime series now closely follows the plot of the manga (even the drawing style is the same as that of manga as well).
In the alchemist world, there exists people with special abilities to manipulate objects and transform one object into another. These people are known as alchemists.
This process does come with a cost though, the basic law of alchemy states that to gain something you have to sacrifice something of the same value.
The main character is the famous alchemist Edward Elric - also known as the Fullmetal Alchemist - who almost lost his little brother, Alphonse, in an accident. Edward managed to contain his brother's soul in a large suit of armor. While he did manage to save his brother's life, he had to pay a great price himself.
To get back what they’ve lost, the brothers embark on a journey to find the Philosophers Stone, a mythical object which would allow them to recover their bodies (which were lost in an attempt to bring their mother back to life through alchemy).