The Moon in your birth chart shows your more spontaneous reactions, what you instinctively seek for a feeling of safety or flee from to avoid a sense of insecurity, in contrast with the Sun, which shows your goal or purpose in life. The Moon in astrology stands for the unconscious in contrast with the conscious, the female rather the male, the emotions rather than the intellect. Just as the Moon without the Sun can show an aimless life bound up with what is felt to be necessary for security, so the Sun without the Moon can show a relentlessly purposeful life pursued solely by the conscious part of one's being without recourse to the great riches of the unconscious.
The Moon waxes and wanes. It was regarded in the ancient world as both treacherous, because the light it provided at night would not last, and as reliable in that it corresponded with the rhythms of life. The Moon phase can correspond with personality types. If you were born just after New Moon, and if other chart factors agree, you may show the Aries characteristics of impulsiveness, seeking to impress yourself on life and on others. If you were born just after Full Moon, the qualities of Libra may show, with concern about how your actions affect others, especially those with whom you are in particular relationships.
Your Moon sign, together with the relationship of the Moon to other planets, will show where you seek security. In Taurus, for instance, this will be physical security, money in the bank, possessions, with good food making you feel good. In Gemini, it will be interaction with others, conversation, knowledge, information gathering without much thought as to whether or not the information is useful (that would be the concern of the Sun).
As reflector of the Sun's light, the Moon can show where you reflect back to the world with motherly concern what you achieve through pursuit of your purpose as shown by the Sun.