shade, protect, cover
廕 centers on providing shelter or protection, like a covering that gives shade. The meanings shade, protect, and cover all express this idea of shielding from exposure or harm.
廕 combines 广 (building, shelter) with 陰, which likely contributes both sound and the idea of shade or concealment. The character expresses protection or covering provided by a structure.
Under a broad roof 广, the shady, protective quality of 陰 (shade, hidden) is at work. Imagine a building casting a cool shadow that covers and protects everything beneath it.
For イン, picture an inn with a wide roof providing shade and shelter: inn -> イン, and the building covers you like 廕.