The meaning :
It means "I bow to Shiva." Shiva is the supreme reality, the inner Self. It is the name given to consciousness that dwells in all. Shiva is the name of your true identity- your self.
According to Hindu mythology there are three Gods who run this creation. The Brahma - who creates the universe, the Vishnu - who preserves the Universe and the Shiva- who in the end destroys the universe. Among the three deities, Shiva, though considered as destroyer, also symbolize the - the inner self which remains intact even after everything ends.
In this mantra the chanter (one who repeats the mantra) bow to Shiva- his true self.
Om Namah Shiva is a very powerful mantra. It has been said about this mantra that if this mantra vibrates continually in your heart, then you have no need to perform austerities, to meditate, or to practise yoga. To repeat this mantra you need no rituals or ceremonies, nor must you repeat it at an auspicious time or in a particular place."