This quote is from Act 3.5. In the opening lines of this scence, Juliet and Romeo have spent their first wedded night together. But it is morning, the time of the lark, and Romeo must fly or face harsh punishment.
Juliet does not want the night to be over. Therefore, she feigns disbelief of the morning, insisting that the birds the lovers hear are nightingales, a bird who sings in the night (thus its name).
Here is the exchange between the two lovers (3.5.1-11):
Wilt thou be gone? it is not yet near day:
It was the nightingale, and not the lark,
That pierced the fearful hollow of thine ear;
Nightly she sings on yon pomegranate-tree:
Believe me, love, it was the nightingale.
It was the lark, the herald of the morn,
No nightingale: look, love, what envious streaks
Do lace the severing clouds in yonder east:
Night's candles are burnt out, and jocund day
Stands tiptoe on the misty mountain tops.
I must be gone and live, or stay and die.