Short answers, pulled from the story.
The Solarium Augusti was a monument in the Campus Martius built in 10 BCE that used an Egyptian obelisk as a gnomon to interact with a calibrated marble pavement. It is now understood to have functioned primarily as a meridian line tracking the noontime position of the Sun across the solar year, rather than as a full sundial as was once believed.
The obelisk came from Heliopolis in ancient Egypt, where it had first been erected under the pharaoh Psamtik II. Augustus transported it to Rome as a monument to his subordination of Egypt to Roman rule.
The 23rd of September was Augustus's birthday. The Solarium and the Ara Pacis were deliberately aligned with the Via Flaminia so the obelisk's shadow would cross the center of the altar on that date, linking the emperor's birth with the theme of Roman peace.
The Solarium was dedicated in 10 BCE, thirty-five years after Julius Caesar's calendar reform. It was the first solar dedication in Rome.
The obelisk was still standing in the eighth century CE but was later thrown down, broken, and buried under sediment. It was rediscovered in 1512 but not excavated at that time. Pope Pius VI had it re-erected in the Piazza di Montecitorio in 1789, where it now stands as the Obelisk of Montecitorio.
Pliny noted that by around 40 CE the Solarium had stopped accurately reflecting the solar year. He offered several possible explanations, including that the Sun, the Earth, or both might not be as fixed in their position and movement as was commonly believed.