ardhanarishvara means the half feminine form of ishvara (Shiva) this form is a combined form of Shiva and Shakti. It is the union of Shiva and shakti and expresses their oneness.

This is one of the most important forms of Shiva described in the shaivagamas, puranas, and mantra shastras

acharya Adishankara bhagavadpada composes this hymn to praise this particular form of Shiva. Worshiping this form is equivalent to worshiping Shiva and Shakti together.
Acharya attaches 2 mantras in the ending verse of each shloka. the Shiva panchakshari (namah shivaya) and shakti panchakshari (namah shivayai) The hymn is an octet comprised of 8 shlokas.

In ardhanarishvara form, a half is feminine & another is masculine, hence he uses words denoting feminine for the it, and the words denoting masculine while referring the masculine half of the form.

He uses same words meaning differently in different contexts and similar words in this hymn n to praise the Shiva portion and the Shakti portion of this form.