The Ceremonial Dagger is a Yautja weapon, used by warriors as a last-resort weapon or a weapon to take trophies from fallen enemies. The Ceremonial Dagger is associated with the Blooding Rite of Young Bloods. It's primary use is to remove the carapace of a Xenomorph but it could also be used as a close-contact weapon if need be. The blade itself is made of either the bones or the 'resin' of a Xenomorph, making it resistant to their acidic blood.
The Ceremonial Dagger attached to the right shins of all three Youngblood Predators in Alien vs Predator. It is treated to be immune against Xenomorph blood. It looks like the trophy which is obtained with this weapon has more value in the Predators' world than other ways of killing a prey, since Celtic let himself open to Grid's attack, just to finish him off in a ritual kill.
In Alien vs. Predator, Celtic was the first Predator to use the Ceremonial Dagger, but died before he could kill a Xenomorph with it. Scar also used a Ceremonial Dagger to make weapons for Lex.
All of the Predators in the McFarlane Toys AVP Series 1 (Celtic Predator, Scar Predator and Elder Predator) feature removable Ceremonial Daggers which are held in a sheath on the figures' right lower leg armour.