Slightly literary. Everyday spoken Chinese prefers 天亮 (tiānliàng, 'sky bright') for dawn. 天明 is more frequent in classical literature, set phrases, and song lyrics. Antonym: 天黑 (tiānhēi, nightfall).
culture
天明 is also a common given name (e.g. former Premier 朱镕基's son 朱云来 — different name, but 天明 is widely used as a male name suggesting bright future). It's also the name of the protagonist in the Chinese animated series 《秦时明月》 (The Legend of Qin).