The Sun in astrology represents one of the fundamental parts of the self: outer awareness. When combined with the sign and house the Sun shows a very large part of our personality. Where does a person gain energy? What are they interested in? We can see this through the Sun in the natal chart.
If you look up at the sky, there are two very bright objects that we use in astrology: the Sun and the Moon. Both are equal in size. They represent two very important aspects of the self. They're both very important.
The Sun's energy is fiery, masculine, and outward. The Sun is the outer awareness, active conscious elements. The moon is the internal and receptive element. When you combine these, you're seeing a very large part of the person's personality. You can see this through the sign and house placement of the Sun.
If you look at the Sun in the sky, it's very bright. It just shines. It doesn't care too much if you're hot. It doesn't care if you're cold. It just shines. This is a very important interpretation of the Sun. It's symbolic of that aspect of the self. The part of the self that just shines, is the way that it is, as the person is.
The Sun is the person's vitality, person's life force, active awareness, and intrigue. What are they interested in, what are they focused on? Since the Sun is such a fundamental aspect of life, it holds all the other masculine energies within it. The Sun is everything that is about vigor, taking action, pursuing, and the outer world focus.
For example, Sun in the eighth house individuals have the awareness of the deeper world. Without even having to think about it they are aware of everything that is behind the surface. The eighth house is everything behind the surface, under the surface, hidden, not seen. But these individuals can see those things, and there's nothing they have to do. They have the natural intrigue for it. They're focused on it, and it's a big part of their personality.
The sign is the way this individual will do it. If it's Gemini then it is through inquisition, through wanting to understand more. Rationally or practically, how does it apply? What does it mean scientifically?
The Sun is a very important part of any chart, especially when you read the house and sign placement. It shows how and what we focus on, gives us energy, and interests us. It is the most fundamental aspect of active consciousness for the individual.