विभूति, vibhūti 
“supreme perfection”, “puissance”, “power”

Sacred ashes obtained either from the sifted ashes left after the homa ritual, or prepared by burning dried cow dung with the addition of milk, honey, ghee and some aromatic substances, followed by consecration in the puja ritual.

It symbolizes purity and is one of the most sacred attributes of ministering to Shiva for all Shaivites. Shaivites (as well as Shaktists) put three horizontal stripes on the forehead with sacred ashes – tripundra, Shaivite tilak. Vibhuti also symbolizes siddhis, mystical powers that develop from the practice of yoga and asceticism.

61. The ashes resulting from Vedic rites in fire shall be smeared over the forehead at the end of the rites. Since the ashes are purified by the mantras the rite itself takes the form of the ashes. 

62-65. Hence, applying the ashes is tantamount to assimilating the sacred rite in one’s own self. Bilva twigs shall be burnt repeating the atma-mantra of Aghora. This fire is called Shivagni. The ashes resulting from this are called Shivagnija. The dung of a cow, preferably of brown or red cow, shall be burnt first and then the twigs of shami, ashvattha, palasha, vata, aragvadha or bilva shall be burnt. The ash resulting therefrom is also Shivagnija. Or the twigs shall be burnt in darbha fire repeating Shiva mantra. After straining the ashes with cloth, it should be placed in a new pot. 

66. For the sake of resplendence, the ashes shall be taken. The word bhasma (ash) means that which is honored and adored. Shiva himself formerly blessed it.

In Nath Tradition, there is a particular bhabhut-diksha related to the application of holy ashes to the whole body.

See also bhasma-dharana.