Getting straight to the point, disregard what the item description says entirely. Bonfire ascetics work by bumping that bonfire's area into the next NG+ level, which has a number of immediate benefits:
- All enemies are respawned
- The respawn counter of all enemies is reset
- Loot on dead bodies is respawned
- Some chests have their loot restored, if they would get any new loot in NG+
- Doors stay open, and any keys you've collected remain effective
- If there are any NG+ enemy types in the area, they will spawn
- NG+ BP enemies and NG+ BP NPCs will spawn in the area (the BP NPCs will not respawn if killed unless another ascetic is burned)
- Enemies have more hp, deal more damage, and drop more souls on death
- If there is a boss within the bonfire's area, it will respawn
- If the boss drops any additional loot in NG+ or higher, it will drop that loot when killed in addition to the loot it normally drops (boss souls, etc)
- Bosses have more hp, deal more damage, and drop more souls on death
You can check how many ascetics you've dropped into a bonfire by selecting the travel option and looking at the little number in the lower right-hand corner of each bonfire's picture. There is no limit to how many times you can burn an ascetic at a particular bonfire, but numbers over 99 are not displayed (credit for this find goes to Callyste).
IMPORTANT NOTE: The effects of burning a bonfire ascetic never wear off. They'll last even when you go into NG+ yourself, and will stack on top of the natural NG+ level. Basically, going into NG+ acts like burning a bonfire ascetic at each and every bonfire, on top of resetting the rest of the game back to its uncompleted state.
As you might guess, this makes them very, very handy for farming. The best places I've found to farm are
Bonfire ascetics are rather rare and sold by some merchants in only limited quantities, but there is one area I've found where you can farm them:
Happy hunting, folks.