Maa Bhuvaneshwari
Om Aim Hreem Sreem Namaha II

O Godess of the phenomenal world (3 lokas/planes and 14 worlds) I bow before you to seek your blessings for wisdom, strength and protection.

Maa Bhuvaneshwari's name lies in the root words Bhuvan (space) and ishwar (sovereign head) . She is the queen of the phenomenal world and is maya. She is space, gyana shakti (knowledge), and the one who governs all animate and inanimate. The divine mother in this form guides one to inner conciousness and to rid ones ownself of maya and to crown ones own self with wisdom and knowledge to do good, to be good and to be more aware and alive and be humane. When we Seek her for divine knowledge She drives consciousness from saguna to nirguna i.e. from understanding the supreme energy with all its physical atributes and moving towards understanding the supreme energy beyond any attribute as infinite.

ॐ ऐं ह्रीं श्रीं त्रिपुर सुंदरीयै नमः॥
Om Aim Hreem Shreem Tripur Sundariyai Namah II 
Surrendering to the Maa Tripura sundari Devi form of Shakti 
Quote:
" cāpaṁ cekṣumayaṁ prasūnaviśikhān pāśāṅkuśaṁ pustakaṁ I māṇikyāṣasṛjavaraṁ maṇīmayīṁ vīṇāṁ sarojadvayaṁ | pāṇibhyāṁ varadā abhayaṁ ca dadhatīṁ brahmādisevyāṁ parāṁ sindūrāruṇa vigrahāṁ bhagavatīṁ tāṁ ṣoḍaśīmāśraye ||

चापं चेक्षुमयं प्रसूनविशिखान् पाशाङ्कुशं पुस्तकं
माणिक्याषसृजवरं मणीमयीं वीणां सरोजद्वयं।
पाणिभ्यां वरदा अभयं च दधतीं ब्रह्मादिसेव्यां परां
सिन्दूरारुण विग्रहां भगवतीं तां षोडशीमाश्रये॥

Meaning: She has twelve hands, holds (1) a bow made of sugarcane, (2) arrows made of kadamba flowers, (3) a noose, (4) a hook, (5) a book, (6) a rosary made of rubies, displays (7) abhaya (removal of fear) and (8) varadha (giving boons) mudras. She closely holds a veena (a musical instrument) with two hands (9 and 10)  and lotus flowers in two hands (11 and 12) one on each side. She is worshipped by Brahmā and other gods and goddesses. She is red in complexion. I surrender unto this Supreme Goddess. "

So what does Maa Tripura Sundar or Shodashi signify?? Here's my simple understanding- The root of her name lies in the word - Tri which means three. She is the most beautiful one in the three worlds ( here beauty is not physical beauty, but the light from spirituality, compassion, eternity, perception, intuition and conciousness). She igintes the three nādi s - iḍā, piṅgala and suṣumna (kundalini); three worlds, bhūr, bhuva, suvaḥ;  three guṇa-s sattvic, rajasic and tamsic.She is also the mother of the three who created the worlds, preserved or destroyed them- Vishnu, Bhrama, Shiva. Knowledge of the supreme self emanates from her when her blessings help in the awakening of the kundalini and ignite one's spiritual connection with the absolute. She is also known as Lalita- the one who plays the divine play of the whole universe. She is also known as Shodashi representing sixteen types of desires and overcoming them for union with the Supreme Brahman. In the form of Raj Rajeshwari she governs the universe as the supreme ruler. 
She gives strength to control the body, mind and ones emotions and to seek liberation. Open your heart to her and she will dwell there with love.

Yaa Devi Sarvabhuteshu Shakti Rupen Sanstitha Namstasye Namstasye Namstasye Namo Namaha
A special day when the Goddess is first adorned with colours marks the end of Pitrupakhshya and the begining of Devipakshya. It is also an invitation from the heart to the Mother Goddess to come down from Kailash mountain to her paternal home with her children. Goddess Parvati, part of Shiva is Shakti and takes many forms to end the existance of Asuras (evil). In other words, It is on Mahalaya she took the form of Goddess Durga and was gifted celestial weapons by all Gods and Godesses to rid of evil. At some point of time, truth and the good always prevails, there is always a catalyst who brings the change and ends the cycle of untruth and evil, whether it is in the mind, the heart , in the metaphysical realm or the real material world. That is the core message of Mahalaya. Let's invoke the good to  take over the evil in us and around us. Let's chant and welcome her.