Nothing. 'Spiritually' is a nonsense word that doesn't really mean anything. However, colours can and do have emotional and cultural significance. For instance, in western cultures, pink is generally for a boy and blue is for a girl. Also, the eye can see more shades of green then any other colour. So there are physiological factors to take into account as well.
The Catholics feel that the color orange represents healing, and your relationship to the external world. In Buddhism, the color orange represents life and vitality, and their nuns and monks wear the color. So in closing, orange is all about your external soul, health, and life.
The color orange means, Praise, Passion, Warfare, Fire, Fruitfulness and Joy among other things. It is a color that is reflected in the rainbow which reflects God's promise to Noah.....(see Genesis 6: 15-17)