SB 10.21.9

gopyaḥ kim ācarad ayaṁ kuśalaṁ sma veṇur
 dāmodarādhara-sudhām api gopikānām
bhuṅkte svayaṁ yad avaśiṣṭa-rasaṁ hradinyo
 hṛṣyat-tvaco ’śru mumucus taravo yathāryaḥ
Word for word: 
gopyaḥ — O gopīs; kim — what; ācarat — performed; ayam — this; kuśalam — auspicious activities; sma — certainly; veṇuḥ — the flute; dāmodara — of Kṛṣṇa; adhara-sudhām — the nectar of the lips; api — even; gopikānām — which is owed to the gopīs; bhuṅkte — enjoys; svayam — independently; yat — from which; avaśiṣṭa — remaining; rasam — the taste only; hradinyaḥ — the rivers; hṛṣyat — feeling jubilant; tvacaḥ — whose bodies; aśru — tears; mumucuḥ — shed; taravaḥ — the trees; yathā — exactly like; āryāḥ — old forefathers.
Translation: 
My dear gopīs, what auspicious activities must the flute have performed to enjoy the nectar of Kṛṣṇa’s lips independently and leave only a taste for us gopīs, for whom that nectar is actually meant! The forefathers of the flute, the bamboo trees, shed tears of pleasure. His mother, the river on whose bank the bamboo was born, feels jubilation, and therefore her blooming lotus flowers are standing like hair on her body.
Purport: 

This translation is quoted from Śrīla Prabhupāda’s Caitanya-caritāmṛta (Antya-līlā 16.140).

In the guise of releasing flowing sap, the bamboo trees are actually crying tears of ecstasy upon seeing their child become an exalted devotee-flute of the Supreme Personality of Godhead, Śrī Kṛṣṇa.

Sanātana Gosvāmī gives an alternate explanation: The trees are crying because they are unhappy at not being able to play with Kṛṣṇa themselves. One may object that the trees in Vṛndāvana should not lament for that which is impossible for them to obtain, just as a beggar certainly doesn’t lament because he is forbidden to meet the king. But the trees are actually just like intelligent persons who suffer when they cannot obtain the goal of life. Thus the trees are crying because they cannot get the nectar of Kṛṣṇa’s lips.