Parvati is the wife of Shiva.
She represents love and devotion. She is also called Shakti, the energy (particularly female energy) of the universe. She is also associated with Durga and sometimes Kali as well. The name Parvati means “she of the mountains.” Since she and Shiva are both associated with austerity and living away from the world, they are connected with mountain living.
It is through Parvati/Shakti that all life energy comes. (In Shakta texts, she is said to ascend beyond even Shiva and is the supreme power of the universe).
Naturally, Parvati’s unique characteristics have become more and more obscured, as she absorbed more and more goddesses into her iconography. Therefore, her depictions have become rather generic today. When shown with Shiva, she carries a blue lotus in full bloom, shows the abhaya mudra (hand gesture of fearlessness) and usually has one of her children on her knee. The only hint of her former occult status is the somewhat languid appearance of her eyes, as one who has recently emerged from deep meditation. Other goddesses are usually shown with large staring eyes as this is considered a mark of beauty. The consorts of the other two Gods of the trinity, Saraswati and Lakshmi, may be depicted alone, but Parvati hasn’t been depicted this way for many centuries.
Parvati is capable of strict discipline and is said to have practiced extremely rigorous austerities to win Shiva’s attention and love.
My favorite story of Parvati is when she stops Shiva from swallowing poison. The story goes that several gods and demons were churning up the ocean looking for a potion of immortality. In the process, many bad things came to the surface, including a toxic poison that would destroy the world. Shiva stepped in and drank the poison to save the world, but his wife ran over and held her hand against his throat, preventing him from swallowing it. And so Shiva has a blue throat, where the poison is contained. (A more detailed telling is here)