Following the initial public assembly, a smaller, more focused gathering took place on the second day of the new year. This day specifically refers to the second day of Rosh Hashanah. During the era of Ezra, an extra day was added to the preceding month of Elul, resulting in a two-day celebration of the holiday [רש״י, מצודת דוד].
Unlike the massive crowds from the day before, this meeting was exclusive. Only the leadership attended, consisting of the priests, the Levites, and the heads of the families who represented the entire population [מצודת דוד, ביאור שטיינזלץ]. The general public did not participate in this specific session [ביאור שטיינזלץ].
These leaders came to Ezra with a clear purpose: to deeply understand the teachings of the Torah. They were not interested in a quick or shallow reading. Instead, they engaged in sincere, heartfelt study aimed at gaining a practical understanding of God's commandments, ensuring that they could actively and properly carry them out [מצודת דוד].