Tara isn't only an important Hindu Goddess but she's also the most important one of the Buddhist tradition. She's a Bodhisattva: that is to say that she had attained Moksha (or liberation from endless re-incarnations) but chose to comeback and re-incarnate in the manifest world to guide and help us all.
She's the first form of Kali (life and time) and related to the power of SOUND (Shabda Shakti) which is seen has the power of time and transformation. She's the divine Word.
In the tradition, Sound is at the source of all creation and therefore transformation. The Word is intelligence of time, whereas Time is the movement of the Word.
Transformation and creativity
Tara comes from the sanskrit root "TRI" which means "to transport" or "take across" in any difficult situation. We call on the Goddess Tara in times of emergencies and deadlock. But "Tara" also means Stars, as the root "TRI" also means "scattered". Thus, she becomes Inspiration, the muse who guides us along the creative path.
Painting in the Dunhuang Series by Zeng Hao
In her manifest form She is the consort of Jupiter, the Vedic lord of Wisdom and the Lord of manifest Sound. She relates to the tongue, she is the power of speech but also our aesthetic mind by allowing us to perceive the essence of all things. She allows Soma (or immortal nectar) to flow into us and is thus connected to the Moon. She has a dual nature by both supporting knowledge (Jupiter) and and ecstasy (the moon). From her relationship to the Moon she gives birth to a son, Mercury, the Planet of Speech and Intelligence.
The 8 serpents she has as ornements stand for the 8 siddhis (which are the 8 magic powers allowing us to transform and fulfil our desires). The scissors she holds represent her ability to cut off all attachements; Her carrying of a lotus flower symbolises her open heart.
In the Body
Tara relates primarily to the Navel Chakra and the tongue. As Om (the Guru), she relates to to the 3rd Eye or the Ajna Chakra. When singing the Mantra it is good to remind yourself she's the current moving from your navel all the way up to your 3rd Eye.
Her bija or seed syllable is OM and could be honoured just by chanting OM. Her longer, 5-syllable-mantra is:
OM HRIIM, STRIIM, HUUM, PHAT
OM is the mantra of deliverance and is the "masculine principle while "Aim", is the feminine). it's energy is uplifting and pacifying. this is the primordial sound, the seed of all things, all all possibilities, the beginnign of any creation
HRIIM is the mantra of purification and transformation, it refers to the Heart (Hridaya in Sanskrit) and is the equivalent of OM for the Goddess. This is the mantra of Shiva's consort. It can be used for all 10 goddesses of the Tantric tradition. The Devi Gita states: "All my worship can be performed with the mantra Hriim. Of all mantras, Hriim is regarded as the supreme guide.
STRIIM is the feminine nature who's power is the give birth. (note: you'll sometimes find "Triim" instead of Striim), it also hold the "ST", for stability.
HUUM is the mantra of divine protection and activation while PHAT destroys obstacles.
How to use the Mantra
Daily, you should repeat the above mantra 108 times (use a Mala, to count each instance) . Below is a video recording of a way to pronounce the mantra.
While repeating it, you should also call upon Tara to remove obstacles for all beings and thereby become Tara yourself.
Another way, is to concentrate on the intervals of silence between each sound and try therefore to hear the silence.
You can help yourself by looking the Tara Yantra while singing the mantra too.
At the root of all through is Om or Tara which takes us to our inner self (Atman) which is pure silence. By signing the mantra everyday we will feel our awareness lifting us effortlessly above obstacles and attachments.
Note: When singing a mantra, be aware each sound has a healing value. They will make your being vibrate at a different frequencies and install a new balance into your physiology. You can refer to Taapoa's post about Sadhguru explaining the value of mantras here to understand more about the value of mantras,
Reference: "Tantric Yoga", by Dr. David Frawley.