Green Tara: the powerful and the most beautiful female form of Buddhist deities

According to the legend, Tara came from a tear drop of Avalokiteshvara (or named Guan Yin in Chinese Buddhism). Though the legend says she vowed to be a companion of Avalokiteshvara, she is in fact another representation of Avalokiteshvara and thus is also a Bodhisattva. Due to her close relation with Avalokiteshvara, she symbolizes great strength and compassion.

In Hinduism, Tara is one of the Mahavidyas (mother goddesses representing the supreme wisdom). According to the Hindu myth, when Shiva was poisoned by the churning of the ocean, motherly Tara appeared and saved him. She wears only a tiger skirt and holds weapons which symbolizes her power and strength.

It is clear that the original symbolism of Tara, motherly love, strength, and power, is borrowed by Buddhism. After relating Tara to Avalokiteshvara, Buddhist Tara is endowed with greater symbolic meaning, such as compassion, individual salvation, and altruistic spirit. In order to develop such spiritual qualities, meditation is required and therefore Tara becomes one of the major tantric deities.

Tara in Buddhism has another significant meaning which helps lift the status of female practitioners. As H.H. the Dalai Lama said:

There is a true feminist movement in Buddhism that relates to the goddess Tārā. Following her cultivation of bodhicitta, the bodhisattva's motivation, she looked upon the situation of those striving towards full awakening and she felt that there were too few people who attained Buddhahood as women. So she vowed, "I have developed bodhicitta as a woman. For all my lifetimes along the path I vow to be born as a woman, and in my final lifetime when I attain Buddhahood, then, too, I will be a woman. (see wikipedia under the category of Tara)

Her mantra is

OM TĀRE TUTTĀRE TURE SVĀHĀ

OM is a sound of respect, of all time, of all space. It does not have any literal meaning but only represents the reality and now.
TĀRE means to seek salvation from mundane dangers.
TUTTĀRE means to seek personal salvation from spiritual sufferings.
TURE means to seek Bodhisattva path in which we not only seek personal enlightenment but also practice great compassion for all who suffers.
SVĀHĀ is to hail and to praise.

As is stated on Wildmind, this mantra is more like a play on the name of Tara (concerning the sound of her name and the sound of the mantra). The website also says that it is better to leave it untranslated since the meaning of original sanskrit is hard to capture and is difficult to express by our normal language now.

Since she is such a powerful goddess who keeps providing great strength to whoever worships her, along with her great mercy to help all to realize their wishes immediately, praying to her should bring us great enlightenment.