Refers to the time around dawn, when the sky begins to lighten. Often used in literary or descriptive contexts.
The birds began to chirp at dawn.
明け方 also means 'dawn' and is more frequently used. 夜明け方 is a slightly more specific or literary variant.
Compound of 夜明け (yoake, 'dawn') + 方 (gata, 'direction' or 'time'). The exact historical derivation is uncertain, but the combination naturally indicates the time of dawn.