Sun Conjunct Moon
The sun represents our vitality and our conscious ego, the self and its expression. It establishes our will to live and our creative force. It is associated with spontaneity and health. A well aspected Sun will describe a person who has heart, who cares for others both in general, and at the personal level. A poorly aspected Sun will describe a person who either has much more difficulty accessing this love and caring ability. In your chart the position of the sign represents your life purpose and style in which your make your mark in the world.
Sun Conjunct Moon
With Sun Conjunct Moon in your Natal Chart means you were born under a New Moon, especially if the orb is less than a few degrees. The classical astrology meaning of a conjunction is that the powers involved merge, so that their characters mix and form a new character, it depends on the planets characteristics as to how this can affect the individual and is one of the most difficult aspects to understand.
In the case of Sun Conjunct Moon, there is a merging of your Vital energies and ego with your emotion self. This can make you quite a stable and centered individual. It can make you more self-centered than normal but its more that you don't need anyone else to make you feel whole (unless your sun and moon is in Libra). But you are very much in touch with your need for others, or at least a significant other.
You can be quite sensitive and emotional; you should look out for transits that may aspect your sun and moon to know when you may be more affected by your moods and emotions. They live and breathe the Sun and the Moon in tandem, so the drive to find a partner is powerful. Because your will and emotions are aligned together you have the ability to know what you want and how to get it with less inner conflicts.
In general, what you desire makes you feel happy and content, you are comfortable with your emotions and are able to express them well unless you have some difficult aspects to your ascendant or sun. The way you manage your own psychological and emotional response to the world might however be quite different when it comes to your intuition about others.
You may have a difficult time understanding why other people seem to get lost in their feelings and are unable to clearly define emotional experience in their lives. Because the Sun and Moon are quite important in defining your personality, having these two planets in the same sign (unless it’s on the cusp) gives much more emphasis on that sign and will be important in defining your personality. You are able to make decisions without too much struggle, simply because it is not their tendency to spread themselves around in order to find all of their options.