Goddess Durga is the consort of Lord Shiva. Her other names are Parvati or Lalita. She exists in various divine - both friendly and fearful forms. Two of her very powerful forms are Durga - the Goddess beyond reach and Kali - the Goddess of destruction. She has a charming personality and is adored by married women for a happy married life.
Both the forms have eight hands and great power and Energy (Shakti). Durga rides on a lion and Kali rides on a corpse of a demon. Kali is the destructive aspect, she is time personified, hence the garland of skull, blood etc.
She is dark because future is beyond one's ken. Her disheveled hair and robes show her non-stop activity. She holds a drawn sword affirming that your and my life is mortal. Her unraised hand shows abhaya for one who has controlled his senses. Her lower hand shows varada-mudra or boon to her devotee.
Parvati was called Sati in her previous divine incarnation.
"Om Sri Durgaya Namah"
This mantra is of Goddess Durga the combined form of the powers of Lakshmi, Saraswati and kali. By enchanting this mantra all the physical, mental, economic problems are solved.
Read Durga Mantras, the songs or shlokas for worshipping Goddess Durga.