So, what a basic but fundamentally important topic.
The best and simplest way to define what the Sun represents in Astrology, and how the different energies of the signs work may be to do a quick comparison of the sun in different signs.
So let's do it!
BUT!!! A key point in identifying and understanding the energy represented by the sun may be to say, 'Without the energy represented by the sign, I feel like I'm dying'.
Sun in Aries: I am direct; I am action; I am to the point.
Sun in Taurus: I am my possessions; I am my things; I am my values.
Sun in Gemini: I am communication; I am thought; I am versatility.
That is the identity/fire quadrant. Identity begins with birth and is identifyable by action. Action is lead by values and the recognition of 'mine', and this needs to be communicated to others.
Sun in Cancer: I am private; I am protected and protection.
Sun in Leo: I am who I am; I am who I express.
Sun in Virgo: I am what I find within; What I find without must conform.
This is the emotional foundation/water quadrant. The formulation of the individual begins in childhood at home then at school. Depending on how secure we feel, we then express ourselves accordingly. Self-expression inevitably leads to the results of behaviour and the attitudes of Virgo.
Sun in Libra: I am my relationships; I must have intimacy.
Sun in Scorpio: I am seeking the purpose of interaction; I am intense.
Sun in Sagittarius: I am living the consequences of relationships/groups.
This is the interpersonal/air quadrant. The development of the individual from Aries to Virgo results in what kinds of relationships can take place. Scorpio indicates the purpose of relations, and Sagittarius is what kind of meaning can be ascribed to those relationships.
Sun in Capricorn: I am in control; I am comprehension.
Sun in Aquarius: I am my principles; I am unpredictable.
Sun in Pisces: I am the result of all previous actions; I am without bounds.
This is the reality/earth quadrant. Capricorn is what others see of us in society, Aquarius the significance of our lives, and Pisces is, like virgo on an individual level, the end result of our social contributions.
To double-check the energy of the Sun in the signs, try this: Imagine each sign placement without the basic energy of that sign, such as a Gemini with no stimulation, or a Capricorn with no serious interaction.
This is a basic comparison, and each placement can be heavily influenced by aspects, transits and progressions.
Who'd like to try doing the Moon through the signs?