Meaning of Aum namah shivai simply means I bow to Shiva or Salutation to Shiva

Aum Namah Shivai (ॐ नमः शिवाय) is the foremost mantra for lord Shiva and is chanted by millions of devotees every day. In the simplest meaning Aum namah shivai simply means
I bow to Shiva or
Salutation to Shiva
But then, the mantras significance goes far beyond its literal meaning. The subtle meaning, the resonance of its sound makes this mantra a maha mantra.
Significance of Mantra
Mantra is general are sounds, syllable, words or a group of words that are capable of performing transformations. When pronounced correctly radiate powerful sound energy. Most of these mantras have originated in Vedas and they have powerful and positive effect on the person who recites them and even on the surrounding environment.
Several of the mantras in Vedas are Japa Mantras (meant for meditation) and they consist of seed letters (बीज अक्ष्रर). These bija-mantra are simple in their layouts and seem to have a equally simple meaning; yet their sound radiate vibrant energy and have a subtle meaning. Aum namah shivaya is one of the finest examples.
The manatra has got two variants –
The Five lettered mantra (पंचाक्षर मंत्र) consisting of letters Na (न), Ma (म), Shi (शि) , va (वा), ya (य) .
The Six lettered mantra (षडाक्षर मंत्र) which is obtained by prefixing the seed letter Aum (ॐ) to the five lettered mantra.
Important to understand, is the fact that each of the letters of this mantra has got special meaning and vibration.
Vibration of Aum namah shivaya
Aum (ॐ)
Aum (ॐ) is the universal sound; it represents the supreme being – the param brahm – Shiva. Aum is a the most important of all bija-mantra and a complete mantra in itself. Yet is used as the begining of most of the Vedic mantras. Aum (ॐ) itself consist of three syllable A (अ) , U (उ) , M (म) and represents conscious, unconscious or dream, and subconscious or deep sleep states. Aum has got another explanations too. But then an entire explanation will require a dedicate volume of works.
Five lettered mantra (पंचाक्षर मंत्र)
The remaining 5 letters, represent the 5 primary elements which constitute the entire universe – Earth, Water, Fire, Air, and Sky (Space).

Na (न) is the sound of earth (पृथ्वी).

Ma (म) effects water factor (जल).

Shi (शि) energises the fire factor (अग्नि)

Va (वा) energises the air factor ( वायु)

Ya (य) energises the space (अंतरिक्ष)
Everything in the universe, including our body is made up of these five basic elements. The sound of each of these 5 letters effects the respective constituents thus causes a positive vibration with purifying effect. Thus the mantra purifies the whole body and the surrounding.

Namah Shivaya represents Transformation
Apart from the positive vibration that the mantra produces, it has got a subtle meaning and significance. Shiva has many aspects – embodied or the personified and a transcendental existence in as formless, attribute less non-being or the universal being.
Na (न) represents the concealing aspect of the Lord Shiva. It is an aspect which is not evident and needs maturity of individuals.
Ma (म) represents the material world and our binding with the material existance. It is in three forms – ego our of ignorance, the cause and reward of karma (work) and illusion (माया).
Shi (शि) represents Shiva himself.
Va (वा) represents the revealing aspect of Shiva; one that is achievable by concentration and maturity. It is the spiritual awakening.

Ya (य) represents the soul. It signifies unification of individual soul to the universal soul. It unifies the chanter with Shiva.
So what is the overall significance? namah shivai is mantra that causes transition from the concealing (not knowing) and materialistic existence to knowing the Shiva, realising him through spiritual awakening and finally attaining him. Thus one who enchants the mantra is sure to achieve Shiva. Note Shiva is the centre and the pivot of the transformation.
Namah Shivai is Shiva
Yet another explanation defines the five lettered word as -
His feet are the letter Na.
His navel is the letter Ma.
His shoulders are the letter Shi.
His mouth, the letter Va.
His radiant cranial centre aloft is Ya.
Thus the five letter defines Shiva. Now how does this explanation go with the previous one. Well they are different ways to explain the same idea. We Start with Na (न) his feet and then subsequently rise to achieve the whole of him.
Namah Shivai negates Ego
One of the final and perhaps the most beautiful way to understand Namah shivai is this way -
Na (न) signifies not or negation. mah (म:) means mine. So Namah (नम:) means not mine. What is not mine? that belongs to Shiva (शिवाय).
Thus this maha-mantra, in its subtle meaning, emphasises negating our ego of possession and moving to the state of being possessed by the supreme being.
Does every thing fit together?
We have come across several meanings of Namah Shivai. Does it seem odd to have so many explanation to a seemingly simple phrase? Not really. Remember one foundation philosophy of Hindus as presented in Vedas and re-emphasised in Gita.
एकं सत्य, विप्राः बहुधा वदन्ति ||

There is only one truth; Wise poeple and sages explain it in different ways.

JAI MAHAKAAL....

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OM NAMAH SHIVAY