The Moon represents your inner emotional nature. Your Moon is what shows you how you process emotions, and how you feel. With a Virgo moon, you prefer to process your feelings logically. You have a practical approach to your emotions, and you do not have overbearing emotional reactions or outbursts. Your emotions aren't chaotic and are generally stable and under your control. You know how to process your feelings rationally and practically.
Virgo Moon makes you very observant of your emotions. You are likely very aware of your emotional nature as you have spent a lot of time in introspection, where you have analyzed your emotions. You know precisely how to process the emotions you feel. A Moon in Virgo is exceptionally beneficial when it comes to analyzing and understanding your own emotions and what you are going through. You can quickly conclude what you are feeling. I.e., say you are experiencing a negative emotion, or something terrible has happened, you will say to yourself "Hold up, maybe I am feeling this way because of x, y, and z, so the reason I am feeling this way now is not really relevant."
You will rationalize your emotions inside yourself, and you will come to some understanding in terms of what you are going through. The Moon in Virgo is a very nice aspect to have as a lot of people do not have their emotions under control, they dont understand their feelings, and they do not know how to work through them. Virgo Moon's generally have their emotions under control, and they do understand them.
It is rare for you to have great outbursts of emotional displays, and your emotions are usually very well organized, like filing cabinets inside you! An excellent way to describe Virgo is to call them the "organizer," and when the Moon that represents our emotions falls in the sign of Virgo, it means that you organize your feelings. You do not let it linger; you do not suppress it and let it boil to the surface to explode. You know precisely how to control your inner emotional world.