Why is pran pratishtha important before an idol becomes a deity?

Pran Pratishtha means infusing life into an idol. Without breath (pran) a human body is nothing. Similarly, an idol is a piece of metal, wood or stone until life is infused into it. This is done through a detailed ceremony by chanting mantras requesting God to reside in the idol. Once this is done the idol becomes deity. Thereafter, it must be bathed, clothed, given ornaments, food, incense sticks and articles of prayer, followed by arti in the morning and evening.

Ganpati Pran Pratishtha Mantra
The Pran Prathista mantra in Sanskrit to be invoked is found in the Rig Veda and is part of Ganesh Suktha.

Gananaam tvam ganapatim havamahe kavim kavinam-upam-shravastamam |

jyeshtharajam brahmanaam brahmanaspata aa nah sharn-vannu-tibhih seeda sadanam || (Rig Veda 2.23.1)

ॐ गणानां त्वा गणपतिं हवामहे कविं कवीनामुपमश्रवस्तमम् ।

ज्येष्ठराजं ब्रह्मणाम् ब्रह्मणस्पत आ नः शृण्वन्नूतिभिःसीदसादनम् ॥

ॐ महागणाधिपतये नमः ॥

We invoke You, O Ganapati of the ganas (Lord Shiva attendants), Who are Brahmana-spati of the brahmas (prayers), the wisest among the wise, Who abound in treasure beyond all measure, the most brilliant one. Please come to us by Listening to our Prayers and be Present in the Seat of this Sacred Sacrificial Altar.. (Rig Veda 2.23.1)

ni shhu sida ganapate ganeshhu tvamahurvipratamam kavinam |

na rite tvat.h kriyate kinchanare mahamarkam maghavan.h chitramarcha || (Rig Veda 10.112.9)

नि षु सीद गणपते गणेषु त्वामाहुर्विप्रतमं कवीनाम्।

न ऋते त्वत्क्रियते किं चनारे महामर्कं मघवञ्चित्रमर्च॥ 

(ऋग् १०-११२-९)

Sit down among the worshippers, O Ganapati, the best sage among the sages. Without You nothing can be done here or far. Accept with honor, O wealthy One, our great and variegated hymns of praise. (Rig Veda 10.112.9)