Vraja Vihari Sri Krishna accepted the mood and complexion of Sri Radha and became Gaura to fulfill three desires:
To understand the greatness of Radha’s love, the wonderful qualities that She alone relishes in Him and the happiness She feels when She realizes the sweetness of His love.
In Vrindavana-lila, Krishna was the witness of the sweetness of Sri Radha’s love of which He Himself was the object, and in Gaura-lila He accepted the mood and luster of Sri Radha to understand the gravity of Her love.
In the opening verse of his book ‘Radha Rasa Sudhanidhi’, Sripada Prabodhananda Sarasvati draws a beautiful picture of how the full transcendental truth of Vraja (Sri Krishna) experienced the sweetness of Radha’s emotions.
Here Sripada follows the custom in the Gaudiya Vaishnava tradition to praise Lord Gaura before commencing the description of Sri-Sri Radha-Madhava’s sweet pastimes.
This is called ‘Gaura candrika’.
In his book ‘Sri Caitanya Candramrta’ (88), Sripada writes:

yatha yatha gaura padaravinde vindeta bhaktim krita punya rasih
tatha tathotsarpati hridyakasmat radha padambhoja sudhambu rasih

“When a very fortunate soul experiences devotion for Lord Gaura’s lotusfeet, the nectarocean from Radha’s lotusfeet suddenly floods his heart.”
Sri Gaurasundara has brought an unprecedented torch of Vraja-rasa, whose bright effulgence shows the devotees the way to the sweet bhajan of Sri Vrindavana,
which is otherwise hard to see. And along with that sweet transcendental Vraja-rasa, Mahaprabhu introduced Himself to the devotees of this world. Sri Vasu Ghosha sings:

yadi gaura na hoto, ki mene hoito,
kemone dharitam de
radhara mahima, prema rasa sima,
jagate janato ke ?

“If Gaura had not come, how would the world have been? Who would have tought the world the greatness of Radha and the limit of prema rasa?”

madhura vrinda- vipina madhuri,
pravesa caturi sara
varaja yuvati, bhavera arati,
sakati hoito kara?

“Who would have shown the way to enter into the sweetness of Vrindavana and the anxious mood of the young girls of Vraja?”

The only way to extinguish the burning sensation of the threefold material misery (caused by the elements, one’s own body or mind,or by other creatures) with a nectar-stream of love for Sri-Sri Radha-Govinda is the mercy of Sriman Mahaprabhu.

– Srila Ananta das Babaji