The characters combine literally to mean “deeply hide, not reveal.” The imagery is powerful: one's true talents are not just hidden, but hidden deeply, far from plain sight, and are deliberately not exposed.
The concept of 深藏不露 is deeply woven into the fabric of Chinese culture, influenced heavily by Taoist and Confucian thought.
This idiom is common in both formal and informal contexts. It is almost always used as a compliment or a statement of respect.