Sun conjunct Saturn in the natal chart means the Sun and Saturn were within 8 degrees of each other when you were born. Because a conjunction places two points in the same part of the sky, the two planets act as a single thing: your core self and Saturn, the planet of limits, discipline, and what gets built through hard work, are inseparable from each other. You do not get one without the other.
The Sun is what you run on. It is where you shine when you are most yourself, the thing that feels like you when life is going well. Saturn is where you are tested. It slows things down, asks for proof, and hands you its rewards only after the work is done. When the two sit in the same place in the chart, those functions merge. Your sense of self is shaped, from early on, by Saturn's demands.
The closer the conjunction, the louder this is. A two-degree orb runs through everything. An eight-degree orb is still there, still real, but quieter in daily life.