There are many levels of understanding – each name of Lalita can be discussed at various levels for hours, I have limited myself to the literal meaning here.
The second verse has physical indicators of Lalita.
E±°ÉlÉÑ-xÉWûxÉëÉpÉÉ cÉiÉÑoÉÉïWÒû-xÉqÉÎluÉiÉÉ |
UÉaÉxuÉÃmÉ-mÉÉzÉÉžÉ ¢üÉåkÉÉMüÉUÉƒ¡ÓûzÉÉåeeuÉsÉÉ ||2||
udyadbhānu-sahasrābhā caturbāhu-samanvitā |
rāgasvarūpa-pāśāḍhyā krodhākārānkuśojjvalā ||2||
qÉlÉÉåÂmÉå¤ÉÑ-MüÉåShQûÉ mÉgcÉiÉlqÉÉ§É-xÉÉrÉMüÉ |
manorupekşu-kodaṇḍā pancatanmātra-sāyakā |
6. E±°ÉlÉÑ-xÉWûxÉëÉpÉÉ (udyadbhānu-sahasrābhā) Brilliance of a thousand rising sunsE±iÉ = rising, pÉÉlÉÑ = sun, xÉWûxÉë = thousand, AûÉpÉÉ = brilliance
Lalita is worshipped in many forms, and the red color is associated with her. The visual of the sky with a thousand rising suns brings up a vivid splash of red.
The Brahmandapurana has described her as having the appearance of the rising sun, and being brilliant.
In the Bhagwad Gita (Ch.11 verse 12) Krishna says that the effulgence of a thousand suns were to blaze forth simultaneously, it would be comparable with the effulgence of the Divine.
7. cÉiÉÑoÉÉïWÒû-xÉqÉÎluÉiÉÉ (caturbāhu-samanvitā) With four handscÉiÉÑ:= four, oÉÉWÒû= arms, xÉqÉÎluÉiÉÉ = she who has
Lalita is described as having four hands. These four hands are the devis whose names are given in the next four names.
8. UÉaÉxuÉÃmÉ-mÉÉzÉÉžÉ (rāgasvarūpa-pāśāḍhyā) Holding the noose of loveUÉaÉ= desires, xuÉÃmÉ = form, mÉÉzÉÉžÉ = noose
Lalita’s upper left hand holds a coral noose with which she can pull the desires of her devotees. This hand is worshipped as Ashwarudha devi who represents icchāśakti (will power) which is at the level of the mind. rāga refers to desires like greed and passion that keep one attached to samsara. Lalita does not let her devotees be ruined by their desires.
9. ¢üÉåkÉÉMüÉUÉƒ¡ÓûzÉÉåeeuÉsÉÉ (krodhākārānkuśojjvalā) With four hands¢üÉåkÉ = anger, AûÉMüÉUÉ = worldly knowledge, Aƒ¡ÓûzÉ = hook to control elephants, EeeuÉsÉÉ = she who shines
The upper right hand of Lalita is worshipped as Sampatkari devi who represent jnānaśakti (knowledge power). krodha represents the anger that stems from our knowledge of undesirability of things, and this discriminatory power of knowledge controls the mind from running after sensory pleasures.
10. qÉlÉÉåÂmÉå¤ÉÑ-MüÉåShQûÉ (manorupekşu-kodaṇḍā) She who wields the sugarcane bow of the mindqÉlÉ = mind, ÂmÉ = form, ¤ÉÑ = sugarcane, MüÉåShQ = bow
The lower left hand of Lalita is Mantrini or Shyamala devi who holds a sugarcane bow.
In the second section, Rudra Samhita, of the Shivamahapurana, there is a reference to the birth of Manmatha in Chapter 2.
11. mÉgcÉiÉlqÉÉ§É-xÉÉrÉMüÉ (pancatanmātra-sāyakā) With four handsmÉgcÉ = five, iÉlqÉÉ§É = five elements, xÉÉrÉMüÉ = having the arrows
The lower right hand of Lalita holds the five arrows of flowers, and is known as Varahi devi.
The five arrows are kamala (lotus) representing excitement, raktakairava (red oleander) representing madness, kalhara (white and red lily) representing confusion, indivara (blue lotus, also called puşkara) representing stimulation, and sahakara (mango flower) flowers representing destruction. Lalita destroys the illusions of her devotees with these flower arrows.
Refer to the Shivamahapurana, the book Rudra Samhita, the section Sati Khanda, where the birth of Kamadeva, the deity of love, is described by Brahma. This attractive mānasa-putra (mind-born son) of Brahma was born with a sugarcane bow and five flower arrows – harşana (thrilling, excitement), recana (madness), mohana (attractiveness causing confusion), śoşana (stimulation) and marana (representing destruction). These arrows would be used to create moha (desire) in the minds of men and women and perpetuate the process of creation. The sages called him Manmatha (he who will confuse minds).
The flower arrows of Lalita are to destroy the delusion in her devotees.
The eminent sage Durvasa was a devout worshipper of Devi. In his Tripura Mahima Stotra, he has written that meditation on the bow, the arrows, the noose and the goad, enables a seeker to stay on the path of spirituality and not get drawn into the illusive samsāra with its worldly attachments.
Refer Yoginihridayam 1-53.
इच्छाशक्तिमयं पाशमङ्कुशं ज्ञानरूपिणम् ।
क्रियाशक्तिमये बाणधनुषी दधदुज्ज्वलम् ॥५३॥
icchāśaktimayam pāśamankuśam jnānarūpiṇam |
kriyāśaktimaye bāṇadhanuş dadhadujjvalam ||53||
The noose that controls desire is icchāśakti, willpower. The goad to control anger is jnānaśakti, the intellect. The bow and arrows represent kriyāśakti, the power of action.
12. ÌlÉeÉÉÂhÉ-mÉëpÉÉmÉÔU-qÉ‹SèoÉë¼ÉhQû-qÉhQûsÉÉ (nijāruṇa-prabhāpūra-majjadbrahmāṇḍa-maṇḍalā) Bathing the universe with her rosy effulgence