When we talk about “conjunctions,” we’re talking about times when from the perspective of an observer on Earth, two planets or a planet and a star approach each other, reach a point where they look like they’re touching or almost touching each other, and then move apart again.
This happens fairly often as the planets travel from East to West across the sky and appear to cross paths with each other and with the stars. The point of closest approach is called a “conjunction,” and is measured in terms of an angle. If we had an arrow pointing right at each of two planets, the angle between the two arrows would define the separation between the planets. This angle is measured in degrees (d), or for the closest conjunctions often in minutes (m) or seconds (s). Sometimes the abbreviations shown in parentheses will be used as shorthand.
Typically the separation of a conjunction needs to be about a half degree (30m) or less in order to be an interesting event. If the conjunction is close enough, it will reach a point where it can no longer be identified as two separate lights in the sky by an observer without a telescope. I’ve read somewhere that this happens at about 100 seconds (1m, 40s) separation. But this varies a bit depending on the brightness of the planets and the eyesight of the observer.
It can be confusing to refer to both time and angle measurements as “seconds,” so the terms “arcseconds” or “seconds of a degree” are sometimes used to avoid confusion when we’re talking about the measure of an angle.