When you're hollowed you look like an undead. You cannot kindle bonfires, see player summon signs or be invaded.
The player becomes hollowed if they die while in human form. A bloodstain will be left at the location of death, but recovering it will not return the player to human status, although it will return the player's lost souls and soft humanity points. Hollowing can be reversed by offering one Humanity at a bonfire.
Hollowing also refers to the process of an undead losing his/her mind. The result of this is seen in the Hollows, Armored Hollows, Undead Soldiers, Balder Knights, and various characters that can go hollow throughout the game.
It seems that having an achievable reason to live or a goal of some kind may be a reason to prevent hollowing as many NPCs1 in the game go hollow as soon as they lose their reason to live, fulfill an objective or are faced with extreme hardships on their quests.