Avatar means incarnation. In Navaratri days all the nine avatars of goddess Durga is worshipped. All these nine forms represent something which is desired by devotees. In Navaratris womanhood is celebrated and worshipped.
Shailaputri (daughter of the mountains)
Goddess Shailaputri is worshipped on the first day of Navaratri. She has two hands. She holds a trident in her right hand and a lotus flower in the left hand. She rides on bull.
She symbolizes the mother nature.
Brahmacharini (pursuer of the sacred religious knowledge)
The goddess is worshipped on the second day of Navaratri. The goddess Brahmacharini wears white clothes, holds a rosary in her right hand and water vessel in her left hand. She appears to be walking barefoot.
She signifies love, loyalty, knowledge and wisdom.
Chandraghanta(who has a half-moon shaped like a bell)
This goddess is the third avatar. Chandraghanta has ten hands where two hands hold a trident, mace, bow-arrow, sword, lotus flower, bell and water-pot, while one of her hands remains in blessing posture. She rides on a tiger or lion, she wears a half moon on her forehead and has a third eye in the middle of her forehead. Her complexion is golden.
She represents war against any form of demon.
Kushmanda ( Goddess of the cosmic egg)
This goddess is worshipped on the fourth day of Navaratri. Ku means "a little", Ushma means "warmth" and Anda means "cosmic egg". She likes the sacrifice of white pumpkin which is called Kushmanda.
She has eight hands holding a trident, discus, sword, hook, mace, bow, arrow and two jars of honey (Elixir) and blood. Her one hand is always in blessing posture. She rides on a tiger.
Skandmata ( Mother of Skanda)
This goddess is the fifth avatar of goddess Durga. Skanda is the another name of War-God Kartikeya, so Skandamata means mother of skanda/Kartikeya.
She is four-armed and rides on a lion. Lord Skanda can be seen in her lap. She possesses four arms out of which two often hold the lotus flowers. One of her hands is always in the blessing posture with the other she holds her son Skanda in her lap. Her complexion is white.
When the devotee worships her, Lord Skand, her son in her lap, is automatically worshipped. Thus, the devotee happens to enjoy the grace of Skandmata along with the grace of Lord Skand.
Katyayani (daughter of Katya)
This goddess is worshipped on the sixth day of Navaratri. She is the daughter of a sage named Katya. She has three eyes and four arms. One arm carries sword, one lotus. The other two are defending and giving blessings. She rides on lion and she is the one who killed Mahisasura. She represents victory over evil.
Kalaratri (goddess of dark night)
This goddess is the seventh, fierce full form of goddess Durga.
Kal or Kala could mean time and black/darkness at the same time. Ratri means night.
Kalratri Devi is the most ferocious form of Goddess Durga. Her complexion is black, she has tousled hair and three eyes. She exhales flames through her nostrils while breathing. She has four arms. She holds a cleaver and a deadly sabre in each of her hands, while her other hands are in giving courage and blessing posture. She rides on donkey.
Mahagauri (goddess of beauty)
Mahagauri is the eighth avatar of goddess. Maha means extremely and Gauri means white/ fair in colour.
She wears white clothes. She has four hands, the hands holding a trident, lotus and drum, while the fourth is in a blessing gesture. The lotus is sometimes replaced with a rosary. She rides a white bull.
Sidhidhatri (goddess of siddhis)
Siddhi means supernatural power or meditative ability, and Dhatri means giver.
She has four hands holding a discus, conch shell, mace, and lotus. She is sitting on a fully bloomed lotus. She possesses eight supernatural powers, called:
Anima- reducing one's body to the size of an atom.
Mahima- expanding one's body to an infinitely large size.
Garima- becoming infinitely heavy.
Laghima- becoming weightless.
Prapti- having omnipresence.
Prakambya- achieving whatever one desire.
Ishitva- possessing absolute lordship.
Vashitva- having the power to subjugate all.