The use of midnight in describing the color brings to mind the darkest blue of the deep night sky. While some have characterized it as closer to indigo, midnight blue is actually a mixture of blue and black, giving it its rich hue.
Midnight blue gets its calming characteristic from blue. While it can give a sense of stability and importance, midnight blue is mostly associated with nature, making it a great choice for a background.
Use bright yellows as an accent to midnight blue, or use it with creams or white for a more traditional feel.