Śrīla Narottama Ṭhākura Mahāśaya starts his glorious book,  Prema-Bhakti-Candrikā, with the following famous verse:

ajñāna-timirāndhasya jñānāñjana-śalākayā |
cakṣur unmīlitaṁ yena tasmai śrī-gurave namaḥ || PBC 1 ||

“I lie prostrate at the lotus feet of Śrī Gurudeva, who has opened my eyes, once blinded by the darkness of ignorance, with the collyrium stick of knowledge.”

I always wondered why Śrīla Narottama Ṭhākura Mahāśaya used the expression “with the collyrium stick of knowledge”.

Our eyes are blinded since beginningless time and by the mercy of Śrī Gurudeva, our eyes can be opened and the darkness of our ignorance can be cast away.

Now, this expression “with the collyrium stick of knowledge” has very deep meanings.

With the collyrium stick of knowledge, Śrī Gurudeva cures the eye disease of the jīvas blinded by ignorance and gives them sight.

In his commentary, Śrī Viśvanātha Cakravartipāda has written the following regarding the ‘collyrium stick of knowledge’:

“kayā unmīlitā jñānāñjana-śalākayā–‘īśvaraḥ paramaḥ kṛṣṇaḥ sac-cid-ānanda-vigrahaḥ, anādir ādir govindaḥ sarva-kāraṇa-kāraṇam ity anena’, ‘kṛṣṇas tu bhagavān svayam ity anena’ ca kṛṣṇa-bhagavattā-jñānam evāñjana-śalākā tayā ‘kṛṣṇe bhagavattā jñāna saṁbitera sāra’ iti śrī-caitanya-caritāmṛtokte.”

Here the word jñāna is understood to mean knowledge that Śrī Kṛṣṇa is himself the Supreme God, and that knowledge is likened to a collyrium stick used to cure the eye of its disease in the form of ignorance. In the beginning of the Brahma-Saṁhitā it is said that Śrī Kṛṣṇa, Śrī Govinda, is the Supreme God; the form of eternity, knowledge and bliss; without beginning; the origin of all and the cause of all causes. This indicates that Śrī Kṛṣṇa is personally Bhagavān, the foundation of all forms of God. In the Śrīmad-Bhāgavata it is written: ete cāṁśa-kalāḥ puṁsaḥ kṛṣṇas tu bhagavān svayam (Bhāg. 1.3.28), meaning that among the various forms of God, some are partial manifestations, and some are parts of those parts, whereas Śrī Kṛṣṇa is Bhagavān Himself. Svayaṁ bhagavān is the Bhāgavata’s own terminology. In other śāstras wherein a form of God other than Śrī Kṛṣṇa is being discussed, this terminology is not used.

With the support of the aforementioned verse, the highly realized ācāryas have deliberated upon kṛṣṇa-tattva and, in their opinion, this is a paribhāṣā, or technical term, for the fundamental truth described in the Śrīmad-Bhāgavata. aniyame niyama-kāriṇī paribhāṣā. “Speech that arranges unsystematized subject matters in an organized way is called paribhāṣā.”

By this device, a word or idea mentioned only once in śāstra can govern countless other words. In the entire Bhāgavata, the kṛṣṇas tu bhagavān svayam verse has been expressed only once. The unrestrained victory flag of this mahāvākya, like that of an emperor, flies gloriously above the heads of all other śāstrika statements.
This knowledge of Kṛṣṇa’s divinity is like a collyrium stick that cures the jīva’s ‘eye disease’ of ignorance.

But this collyrium stick also has a very rasika-meaning, a meaning which is very deep and essential for the hearts of the Gaudiya Vaishnavas.

By using this expressuion “collyrium stick”,  Śrīla Narottama Ṭhākura Mahāśaya secretly hints at the highest gift Sriman Mahaprabhu came to give us and at the highest knowledge that can be bestowed:

anarpita-carim cirat karunayavatirnah kalau
samarpayitum unnatojjvala-rasam sva-bhakti-sriyam
harih purata-sundara-dyuti-kadamba-sandipitah
sada hrdaya-kandare sphuratu vah saci-nandanah

“May the Supreme Lord who is known as the son of Srimati Saci-devi be transcendentally situated in the innermost chambers of your heart. Resplendent with the radiance of molten gold, He has appeared in the Age of Kali by His causeless mercy to bestow what no incarnation has ever offered before: the most sublime and radiant mellow of devotional service, the mellow of conjugal love.”
(Sri Caitanya-caritamrta Adi 1.4)

Conjugal love (mādhurya-rasa) is also known as śṛṅgāra-rasa.
śṛṅgāra actually means  to “decorate”.

śrī-vigrahārādhana-nitya-nānā-
śṛńgāra-tan-mandira-mārjanādau
yuktasya bhaktāḿś ca niyuñjato ‘pi
vande guroḥ śrī-caraṇāravindam

The collyrium stick is used by Srimati Radhika to attract Śrī Kṛṣṇa. She decorates Herself only to give Him the utmost pleasure. The goal of this particular collyrium stick of Hers is to invite  Śrī Kṛṣṇa to kiss Her.

The Gaudiya Vaishnavas aspire to become maidservants of Srimati Radhika and it is our life and soul to assist Her, to serve Her and to help Her achieve Her goal – to enchant Śrī Kṛṣṇa.

So, “with the collyrium stick of knowledge”, Sri Gurudeva also opens our spiritual eyes and the knowledge here also refers to the knowledge of our eternal spiritual form as a maidservant of Srimati Radhika and to the knowledge of our duty to help Her decorate Herself to please Śrī Kṛṣṇa, for example with a wonderful stick of collyrium.
The maidservant´s existence lies solely in this duty to Her beloved Svamini.