Humunculi are creatures that are immortal to a degree, and have a wide range of special powers, but are unable to use alchemy. They carry a resemblance to the person that they were meant to be, and have, in some instances, fragments of memories and personality that once belonged to the original person. They aren't human by any definition, however, and have overwhelming destructive tendencies. They usually possess an indifference or hatred of humans and will not hesitate to kill.
In the series, their are seven Humunculi all representing one of the seven deadly sins in the Bible. They have personalities and powers to match their names, and often have a back story to support it. For example, Gluttony has the ability to eat anything, and will not hesitate to do so. He's seen as being short, overweight, but as a Humunculus he's incredibly strong as well. He is simple minded, and very dangerous. He truly lives up to his name.
In the world of Fullmetal Alchemist alchemy can be used to change the shape of the material that one has on hand. Given enough skill one can take raw ore and purify it into iron ingots, and even shape that material into whatever the alchemist desires. An example of this would be Edwards' mechanical arm. He's seen shaping it into a blade many times throughout the series.
A Homunculus, however, is the result of an alchemist trying to revive the dead by gathering all the ingredients that people are made of, and using alchemy to arrange the matter into a person. In doing so a price has to be paid, usually sacrificing a limb or the caster's life. In the case of the Elric brothers, Alphonse and Edward attempted to revive their dead mother; resulting in Alphonse losing his body as the payment, and Edward sacrificing one of his limbs. They did succeed in bringing to life a Humunculus, but it wasn't their mother. Far from it, in the original anime series it's alluded to that they brought to life a monster instead long before the Humunculus is introduced.