The same degree, and a planet you could not see
A conjunction is two bodies at the same ecliptic longitude, and eight degrees of orb is allowed. The Sun advances about one degree a day, so it stays within eight degrees of the slow moving Saturn for roughly a fortnight either side of the exact contact.
This happens once in each solar to Saturn cycle, which runs about 378 days, so a little less often than annually. That gives a window of about a month in every thirteen, which is why the aspect turns up in charts fairly regularly.
There is an astronomical fact behind it that no other Saturn aspect has. At conjunction Saturn is on the far side of the Sun from us, or nearly so, and it is lost in the glare. For weeks around your birth Saturn was not visible from Earth at all. Older astrology took that literally, and the invisibility is the root of much of what gets said about the aspect.
What the tradition reads into the fusion
The Sun stands for conscious purpose, vitality and the account you give of yourself. Saturn stands for limit, time, obligation and the thing that does not yield to enthusiasm. A conjunction does not put these in dialogue, it fuses them, so the limit is not something applied to the identity from outside. It is part of the identity.
The standard description is early responsibility, a low tolerance for showing off, and a sense of one's own worth that is tied to what has actually been done rather than what could be. Older texts are harsher and speak of a burdened solar principle. Modern readings tend to focus on authority: the person either becomes an authority themselves or spends a long time negotiating with one.
What is consistent across sources is that the aspect is not read as short of energy. It is read as energy that arrives with conditions attached, so nothing about it is casual and very little of it is fast.
Orb, sign and house
Inside two degrees this is one of the more legible aspects in astrology, in the sense that people with it usually agree with the description before they know what it is. Between five and eight it thins out considerably, and a Sun eight degrees off a Saturn in the following sign is barely a conjunction in most practitioners' hands.
Sign changes the tone sharply. In Capricorn or Aquarius, Saturn is in its traditional rulership and the fusion reads as competence and containment. In Leo or Cancer, the signs opposite those, the same aspect is usually read as a much more uncomfortable arrangement, since the Sun is strong in Leo and Saturn is not.
House says what area of life carries it. In the tenth it is the textbook version and is read as career and public standing. In the fourth it is domestic and is often connected to a parent. In the twelfth it is largely invisible to other people, which is a very different thing to live with.
Cycles worth knowing, and reading your own
Saturn takes about twenty nine and a half years to circle the zodiac, which is where the Saturn return comes from. For anyone with this conjunction the return is not just Saturn coming home, it is Saturn returning to the natal Sun's degree as well, and most astrologers treat that as a doubled event around the ages of twenty nine and fifty eight.
Saturn is retrograde for about four and a half months in each year, but it cannot be retrograde at an exact conjunction with the Sun. Retrograde motion happens around opposition, so a natal Sun conjunct Saturn always has a direct Saturn, which is one of the few clean rules in this area.
The widget above reports your exact orb, the shared sign and the house, and those three figures decide which version of the description applies to you.
Questions people ask about this
Was Saturn visible when I was born?
Almost certainly not. At a conjunction Saturn lies close to the Sun in the sky and is lost in daylight and twilight glare for weeks either side. That invisibility is the astronomical fact behind much of the traditional symbolism for this aspect.
How wide can the orb be?
Eight degrees is the standard for a conjunction. Since the Sun covers about a degree a day and Saturn barely moves, that window lasts roughly a fortnight on each side of exact. Inside two degrees the aspect is usually a defining feature of the chart.
Can Saturn be retrograde in this aspect?
No. Outer planets go retrograde around their opposition to the Sun, not their conjunction, so a natal Sun conjunct Saturn always has Saturn moving direct. A wide conjunction near the edge of orb is the only place this gets ambiguous.
Is Sun conjunct Saturn a hard aspect?
Conjunctions are neither hard nor soft by classification. They intensify whatever they join. With these two bodies the result is usually described as serious and slow rather than easy or difficult, and the sign involved does a great deal to set the tone.
What happens at the Saturn return with this aspect?
Saturn returns to its natal degree at about twenty nine and again near fifty eight. Because the natal Sun sits at the same degree, transiting Saturn conjoins both at once, and most astrologers read that as an unusually pointed version of an already significant period.
How common is Sun conjunct Saturn?
Reasonably common. The Sun and Saturn come to conjunction about once every 378 days, and the eight degree orb covers roughly a month of that cycle, so a noticeable share of charts contain it in some form.