Sun
In astrology, the Sun is the center of the chart and what people usually call "your sign": when someone says "I'm a Leo," they mean the position of the Sun.
Governs
The Sun governs the core of the personality: will, life direction, who a person wants to be and what they consider their own. It is not the whole character but its backbone, what shows up in important decisions and in crises.
In traditional astrology, the Sun is associated with the father, authority, creativity and health in the sense of vitality. Its cycle is one year, so everyone born in a given month shares the same Sun sign.
In the signs and houses
The Sun's sign sets the way the will is expressed: direct in Aries, evasive in Pisces. All twelve signs describe exactly this part.
The Sun's house in the birth chart shows the area of life where a person shines brightest: in the tenth, career; in the fifth, creativity; in the seventh, partnership.
Strong and weak placements
Domicile: Leo; exaltation: Aries. Detriment: Aquarius; fall: Libra.
These are terms of classical astrology: "domicile" means the planet is in its own sign and expresses itself freely; "fall" means it struggles. These assessments have no testable basis: they are the internal logic of the system, established as far back as the Hellenistic period.