When you're hollowed, you look like an undead. You cannot kindle bonfires, see summon signs or be invaded.
The player character is hollowed at the start of the game and becomes hollowed again if they die while in human form. A blood stain will be left at the location of death; recovering it won't return the character to human form, but it will return the lost souls and soft humanity points. Hollowing can be reversed by offering one Humanity at a bonfire (reverse-hollowing)1 .
Some online Multiplayer Items require human form and thus cannot be used by hollows: Cracked Red Eye Orbs, Red Sign Soapstone, Eyes of Death and the Red Eye Orb.
While hollowed, Item Discovery and Curse resistances are unchanged, only the amount of soft humanity in the humanity counter can change these values, being human or hollow makes no difference.
Hollowing also refers to the process of an undead losing their 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 prevent hollowing, as many NPCs2 in the game go hollow and become hostile as soon as they lose their reason to live, fulfill an objective or are faced with extreme hardships on their quests.