Sun in 3rd House
When your sun is in your third house you strongly identify with what you say and how you communicate with others. You see yourself as a reflection of your mental agility and your communication style and you may well define yourself by how you are able to communicate who you are to the world around you. Your mind and your mental processes are deeply important to you and you see your thoughts and your ability to express them as your identity.
You are drawn to studying a variety of subjects but often find it difficult to stay with a single one. The result is that you know a bit about everything which works well for you because your sense of value comes from being the go to person for information. You work hard to keep abreast of new trends, ideas, subjects and activities so that you are able to stay constantly engaged with the world around you. With this placement it is very likely that you gauge your worth by your mental capacity, if you see yourself as smart then you consider yourself worthy, but if you believe that you are not intelligent then you may face deep seated self judgement about your place in the world.
In astrology the sun represents the self, the ego, character, individuality and the unique gift that one has to offer the world. When most of us begin to study astrology we start with getting a better understanding of our sun sign and in popular culture when you ask someone what their astrological sign is they almost always respond by telling you their sun sign. Most people who have studied astrology in any depth understand that the sun is but one variable of many but because your sun represents how you see yourself and arguably who you are on a soul level it is a significant factor in your chart.
The third house is also the house of your self effort. Meaning that this house controls how you put yourself out into the world and your capacity to take responsibility for your own experience. With the sun in this house you likely define your success almost exclusively by your own efforts. You see everything that you have put into your life and account any success or failure to your own behaviour. This perception means that your sense of self can be largely reliant on your concept of success or failure.
Sun in the 3rd House
You need activity and a change of scenery often, or you feel restless. You take pride in your mental agility and your friendships. You are able to adapt quite easily to whatever environment you’re in. There is a strong need to communicate your knowledge to others and to learn. Your curiosity is endless. Take pride in your intellectual or communicative abilities without feeling the need to lord it over others or to always be "in the know".
Alternate Interpretation: You get off to a fast start in life. You expect to be good at what you do. You see competency as primarily a matter of experience, and you set out to gather a broad understanding of people, your environment and life in your early years. The natural lines of growth in life show that you concentrate on communication and learning as your self-picture develops.