Innocence is used by Exorcists chosen by the Innocence to wield them (they appear to them in a form of a humanoid or animal-like creature). Each piece of innocence is different and is specifically created for their use. Innocence is somewhat sentient and can make up it's own mind who it will use as a host or something else.
The Earl crushes a shard of Innocence easily.
One part of the Black Order's agenda is to find all of the Innocence shards as well as their compatible users to defeat the Earl and his followers. The Innocence is the only thing that can destroy Akuma without destroying its soul, and hurt the Earl and members of the Noah Family, the Noah and Earl have the ability to destroy shards of Innocence by crushing them in their hands. At least 12 pieces of Innocence have been destroyed by them so far.
If a piece of Innocence has decided that the one using it has sinned or will not recognize the current user anymore as it's master, the exorcist will become a Fallen One. This is where the Innocence completely takes over an exorcist's body and turns it into a monster, destroying everything surrounding it. There is no current cure for this and eventually the one afflicted will burn out and die in 24 hours. Allen managed to stop Suman, a fallen one, by removing the Innocence itself from him but by then Suman's mind was already dead and he had become a comatose, non-responsive person.