śrī-śuka uvāca
ity ādiṣṭā bhagavatā
labdha-kāmāḥ kumārikāḥ
dhyāyantyas tat-padāmbhojam
kṛcchrān nirviviśur vrajam
sri-sukah uvaca -- Sri Sukadeva Gosvami said; iti -- thus; adishtah -- instructed; bhagavata -- by the Supreme Personality of Godhead; labdha -- having obtained; kamah -- their desire; kumarikah -- the young girls; dhyayantyah -- meditating; tat -- His; pada-ambhojam -- upon the lotus feet; kricchrat -- with difficulty; nirvivisuh -- they returned; vrajam -- to the cowherd village.
The gopis' desire was fulfilled because Lord Krishna had agreed to act as their husband. A young girl can never spend the night with any man except her husband, and thus when Krishna agreed to engage the girls in the nocturnal rasa dance during the coming autumn season, in effect He was agreeing to reciprocate their love for Him in the role of a husband.