The holy Ash is the substance the devotees wear on their bodies with adoration and respect. This along with the rudrAxa beads (1) shows up the devotees of the Simple but Supreme Lord shiva. The holy Ash has lots of spiritual sense. There are lots of hymns telling the glory of the holy Ash. ((2) - for example). Ash - the substance that is arrived when things are completely burnt off. In natural terms it is a final state. The state where it has nothing left to burn off ! This indicates the transience of the beings and the Permanence of the Supreme that smears in this ash. This also indicates the matured state of bliss the devotees would be heading towards which stands beyond perturbance - transformation (nothing to burn off).

In the Veda, Rudra Ganas are hailed as “निलग्रीवाः शितिकण्ठाः” (with blue throat, ash smeared white throat).

Bhasma tripundra vidhi in the Shankhayana Grihya Sutra: सौपर्णव्रतभाषितं दृष्टं वृद्धसंप्रदायानुष्ठितं त्र्यायुषं पञ्चभिर्मन्त्रैः प्रतिमन्त्रं ललाटे हृदये दक्षिणस्कन्धे वामे च ततः पृष्ठे च पञ्चसु भस्मना त्रिपुण्ड्रं करोति(6) (The Suparna vow is stated. According to the tradition of the elders, five mantras are used to apply the Tripundra with ash at five points - the forehead, heart, right shoulder, left shoulder, and then the back.) 

Narayana Bhashya: कीदृशं त्रिपुण्ड्रं सौपणंव्रते परिशिष्टे भाषितं । पुनः कीदृशं वृद्धसंप्रदायैः पूर्वैः ऋषिभिरनुष्ठितं कृतं । उक्तं च वीरभद्रपद्धतौ -  ह्यायुष्याणि कुरुते भस्मना ललाटे दक्षिणांसे तथा सव्यहृत्कंठे त्र्यायुषमिति प्रतिमंत्रं । त्र्यायुष्याणि त्रिपुण्ड्राणि । पद्मपुराणे शंभुवचनं रामं प्रति पापं नाशयते कृत्स्नमपि जन्मशताज्जितं । भस्मनात्सर्वपापानां स्मरणाच्च महेशितुः । भस्मेति च समाख्यातं, तस्य धारण- मुत्तमं ॥ यथाविधि ललाटे वै वह्निस्य प्रचारणात्। नाशयेल्लिखितां यामी पटस्थामिव हव्यभुक् । कण्ठे च धारणात्कंठभोगादिकृत पातकं बाह्वोर्बाहुकृतं पापं वक्षसि मनसा कृतं । नाभ्यां शिश्नकृतं पापं पृष्ठे गुदकृतं तथा पाश्वपोषरणाद्राम परस्त्रया लिंगनादिजम् । तद्भस्मधारणं शस्तं सर्वत्रैव त्रिपुण्ड्रकम् । ब्रह्मविष्णुमहेशानां श्रव्यग्नीनां च प्रधारणम् । गुणलोकत्रयाणां च धारणं तेन वै कृतमिति । कालाग्निरुद्रोपनिषदि । मानस्तोक इति समुद्धृत्य शं नो देवीरिति ज्यायुषमिति च शिरो लाटवक्षस्कंधेष्विति त्रिभित्र्यायुषस्त्रयंबके स्तिस्रो रेखाः प्रकुर्वेतेति । त्रिपुण्ड्रं ब्राह्मणो विद्वान्मनसापि न लंघपेत् । श्रुत्या विधीयते यस्मात्तत्यागी पतितो भवेत् ।  मध्यमानामिकांगुष्ठैः ललाटे भस्मना कृतम् । तत्त्रिपुण्ड्रं भवेच्छंखं महापातकनाशनं । इति लौगाक्षिसूत्रे । बृहन्नारदीये त्रिपुण्ड्रधारिणो ये वै ते च भागवतोत्तमाः । द्राक्षालंकृता ये च विष्णुनामाभियंत्रिताः । इति । (What kind of Tripundra is described in the Suparna vow appendix? And what kind was practiced by the ancient sages in the old tradition? As stated in the Virabhadra manual - "One should apply the ash marks for longevity on the forehead, right shoulder, left heart-region and throat, reciting the Tryayusham mantra for each mark. The three marks of ash are called Tryayushyani (three marks of longevity).")

The purANic events associated with the holy Ash show its significance. When the three daemons of impurities (tripura) were burnt down by the mere smile of the God, the ash that remained got settled on the Lord, Who danced there. Thus the tripurAri was smeared in the Ash that came out of burning out of the three impurities. When the cupid - the deva of lust, tried to fire his arrows on the yogic Lord, he was burnt by the Lord into a heap of ash. The unruffled Lord appeared decorated with that ash. At the times when everything reduces unto It, the Everexistant Lord wears that ash.

In the Padma Purana, पद्मपुराणम्/खण्डः ५ (पातालखण्डः)/अध्यायः १०५   Lord Shambhu tells Rama: "The ash destroys all sins accumulated over hundreds of births. Through ash and remembrance of Maheshvara (Shiva), all sins are destroyed. This is called 'Bhasma' (sacred ash) and wearing it is considered supreme. When applied properly on the forehead according to ritual, it destroys sins just as fire consumes offerings. Wearing it on the throat destroys sins committed through the throat, on the arms destroys sins done by hands, on the chest destroys mental sins, on the navel destroys sins of lust, and on the back destroys related sins. O Rama, wearing the three lines of ash everywhere is recommended."

The devotees of the Lord, Who gives His form to the ardent worshipper, wear the same way the holy Ash on their body. This holy Ash is prepared in the ritual fire in a specified way (3) along with the chanting of the Holy Five Letters (4) and other vedic hymns. Thus obtained Holy Ash is worn on various specified places of the body including the forehead chanting the Holy Five Letters. (There are two broad categories of wearing the Holy Ash. One is uddUlanam that is sprinkling the Holy Ash on the body and the other is tripuNDram that is in three distinct bands)

Some of the upanishads that hail the glory of holy ash.

• kAlAgnirudram
• taitrIya
• yogatattva
• jApAli
• sanyAsa
• vAsudeva
• bhasmajApAla
• jApAla (bR^ihajjApAla)
• nArada parivrAja
• rAmarahasya
• chANDilya
• tripurAtApini
• atharvashira

See Also:
1. rudrAxam 
2. Holy Ash padhikam of thirunyAnachamban^dhar
3. Making and Glory of Holy Ash from periya purANam
4. The Holy Five Letters
5. bhasma jAbAla upanishad