First we will see the meaning of navratra . nav means nine and ratra means night.
In Hinduism, Durga (Sanskrit: "the inaccessible" or "the invincible") or Maa Durga (Mother Durga) is a form of Devi, the supreme goddess. Goddess Durga is the mother of Ganesha, Kartikeya. She is thus considered the fiercer, demon-fighting form of Shiva's wife, goddess Parvati.
Nine also a divine number ,nine is a divine shakti. In these nine days we do a puja of nine devis and get blessed by them. Maa durga is a maha shakti who is a goddess of gods. Worshiping of this divine helps us to overcome from our sins.

Puja vidhi

The Hindu festival of Navratri is celebrated twice a year. The first Navratri of the year is known as Chaitra Navratra, as it falls in March-April. The second Navratri is held in October-November, which coincides Durga Puja. The nights of Navratri are devoted to the reverence of Goddess Durga, who is worshipped in many forms. Prayers are offered to Goddess Durga, as she is considered the manifestation of the absolute energy that pervades the Universe. All through the nine days, a person should  chant mantras, sing songs and bhajans in the praise of the deity to get undue benefit from the maa. Fasting on Navratri is considered auspicious. To celebrate the festival, a number of pujas are conducted all through the nine days. Go through the following lines to get the vidhi (procedure) of Navratri pooja.

The devis roops are and mantra that should be recited on that day :

1 maa shailputri                         : Vande vaanchhit laabhaaya chandrardha krita shekharaam!Vrishaarudham shuladharam Shaila-putrim yashasvinim!!

2 maa brahmachaarini                    : Namoh devyai mahadevyai shivayai satatam      namahNamah prakrutyai bhadraayai niyataah pranataahsma ta

3 maa chandrakanta                      : OM Chandraghanta Chandi Rakhsa

                                                          Karo OM Bhayaharini Maiya Rakhsa Karo

OM Nav Durga Namah

OM Jag-Jana-ni Namah

4 maa kushmaanda                           : OM Kushmanda Tum Hi Rakhsa Karo OM Shakthirupa Maiya Rakhsa Karo

OM Nav Durga Namah

OM Jag-Jana-ni Namah

5 skand maa                                            : !! OM Skandmata Mata Maiya Rakhsa Karo !!
!! OM Jagadamba Jana-ni Rakhsa Karo !!    OM Nav Durga Namah                                                  OM Jag-Jana-ni Namah

6 maa kaatyani                                                      : OM Kaatyayani Maiya Rakhsa Karo
                                                               OM Pap-nashini Ambe Rakhsa Karo

7 maa kaalratri                                                     :  OM Kaalratri Kali Rakhsa Karo !!
!! OM Sukhadati Maiya Rakhsa Karo                                                                                                                                                                     OM Nav Durga Nam

 OM Jag-Jana-ni Namah

8 maa mahagauri                                                 : !! OM Mahagauri Maiya Rakhsa Karo !!
                                                                                                              !! OM Bhaktidati Rakhsa Karo !!
9 maa sidhiratri                                                   : !! OM Siddhiratri Maiya Rakhsa Karo !!
                                                                                                             !! OM Nav Durga Devi Rakhsa Karo !!
                                                                                                             !! OM Nav Durga Namah !!
                                                                                                             !! OM Jag-Jana-ni Namah !!
Navaratri Puja Vidhi

Certain items are required to perform the Navratri pooja. These may include the idol or picture of Goddess Durga, Durga Sapthashati book, water in Kalash (pitcher), fresh washed mango leaves, one coconut, roli (red color for tilak), moli (red sacred thread), chawal (rice), paan (betel leaves), supari (beetle nuts), cloves, cardamom, kumkum (vermilion) . You will also need few incense sticks, a deep and matchstick. The flowers used for Navratri puja may include rose, lotus and red hibiscus. Stalks of Bilwa (bael) leaves are also used for the puja. You may offer fresh pomegranate and sweets such as laddoo and peda, as prasad. You will require a Panchpatra containing spoon and water, bael leaves. Take a mat as well, to sit.

In order to perform the puja, take bath in the morning and wear laundered clothes. Then, fill the kalash with water and place mango leaves on its mouth. Place a coconut inside the kalash. Now, tie moli on the neck of the pitcher. Place the idol or picture of Ma Durga at your puja room and then worship the deity with roli, rice, flowers, balepatra, kumkum and gulal. Thereafter, you may add burning coal to a clay pot and pour ghee (clarified butter) over it. Offer a small piece of the sweetmeat to the fire. Keep adding ghee to the fire at regular intervals. Make sure that you maintain the light throughout your puja. Once the puja is over, fold your hands and encircle the flame for three times. Light the incense sticks and deep and perform the aarti. You may sing arti song while doing the aarti. You may chant Durga Saptashati or Devi Kavach or ask a pundit to do it, to conclude the puja.