Rite of Kindling is a special utility item in Dark Souls.
The Rite of Kindling is lost with every playthrough, but kindled bonfires remain at the level that they were bolstered. Therefore, it is a good idea to kindle important bonfires before moving to NG+, as it may be quite a while before players have access to the Rite of Kindling again.
Any bonfires that were previously kindled just twice before going into NG+ (i.e. 15 estus flasks), when encountered in NG+, can be kindled a third time (to 20 estus flasks) without having to first reacquire the rite of kindling.
Reah of Thorolund and her followers were seeking the Rite of Kindling, which was also the reason why they went down into the Catacombs. Strangely enough, they traveled past the point where the rite is found (off Pinwheel) and ended up in the Tomb of the Giants, where most of them met their demise.