The Dried Finger can only be picked up once, the player won't be able to pick it up in the next playthroughs again. However, it can't be dropped and won't disappear in a NG+.
In Dark Souls, there is a special invasion timer that starts to count down every time you complete a fight where someone invaded your world, whether you win it or lose it. It is set to around 10 minutes, and no one can invade your world until it has depleted. Once picked up, the Dried Finger can be used unlimited times to reset the invasion timer to zero, allowing the player to get invaded more often.
The Dried Finger is a highly valuable PvP item, as it allows the player to get invaded much more often in several places where people often invade. These places are for example generally everywhere in Anor Londo, Darkroot Garden or the Kiln of the First Flame.
- Since this item is finger with "multiple knuckles" and is "shriveled but still slightly warm", it's possible that it was a piece of an Undead Dragon, a creature that died long ago but is kept alive (thus "warm") even if horribly rotten.