Hollow Ichigo is the true form of Ichigo Kurosaki's zanpakutō, Zangetsu. He was born from the Hollow called White that merged with Ichigo's latent Soul Reaper powers to become his zanpakutō.
He is an entity existing inside Ichigo's spirit. His name is not "Hollow Ichigo" despite called like this, he is never refered as such in the manga. He is usually called "him", "he" or "that". Also despite his "name" and appearence he is not an ACTUAL hollow, as he doesn't have a mask or a hole in the chest like other hollows, and he doesn't eat other's souls, but on the other hand, it's clear he is part of Ichigo's soul infected by the hollow's realm and manifests himself as a hollow mask in the corporeal plane. Even he himself doesn't know what he really is. He stated he doesn't know his name and during the Bount Arc, when asked who he is, he says "I am who I am!".
Hollow Ichigo is a dark, nightmarish and distorted version of Ichigo, with psycotic grins over his face. He taunts and belittles Ichigo over what he believes to be his weakness, to fight with logic, rather than instinct. Still, he relishes the idea of having Ichigo's powers as his own. He views himself as a horse and Ichigo as the king, because Ichigo is in the control of their shared body, but he doesn't like the idea of carrying a king, who is weaker than himself, and get cut to ribbons with him, so he wants to become the king and take control of Ichigo's body.
When Ichigo defeats him, he proves to dominant, and so the Hollow Ichigo accepts to become his horse... for the meantime, but promises he will return if Ichigo "messes up" and he will try to take control again.
In the final arc it's revaled that he is the real Zangetsu and the other one pretenting to be zangetsu is actuality ichigo's quincy powers who have taken the form of Yhwach from 1000 years ago.
Special Ability: Zangetsu's special ability is getsuga tensho, an enhanced version of shikai's getsuga tensho. When used with his Bankai, these blasts are white with a red outline and their path can be controlled, with a lot of power and speed than getsuga tensho. During Byakuya Kuchiki's fight with Ichigo, the Hollow took control over ichigo kurosaki and was the first person or hollow to do it. Thus, the more Ichigo used this move, the easier the hollow to take over ichigo and take control of ichigo's body. It is assumed that hollow ichigo learned to contain getsuga tensho just like ichigo when he learned it, giving each blow the power of getsuga tensho.