to rise or come up into view: the sun climbs the sky, light breaks over the horizon, a cloud lifts, or a person springs up like a fresh shoot
At its plainest this word watches something climb into view. The sun clears the horizon, a cloud builds in the west, and the same verb reports both.
The Bible then stretches that picture. When a light "dawns" on people sitting in darkness, or a morning star "rises" in the heart, the sunrise becomes an image of rescue breaking in. And when Hebrews says the Lord has "sprung" from Judah, the word shifts from the sky to a family tree: a person comes up like a fresh shoot from its stock, echoing the promised Branch that would spring up (צָמַח) in the Hebrew prophets.
The closely related noun (ἀνατολή) carries the same idea frozen into a thing: the "rising" itself, the east where the sun comes up, and even the "Dayspring" who visits from on high.