Overall meaning:
It was the regular practice of the Prophet ﷺ and of his Rightly-Guided Caliphs to lead the people in the two Eid prayers—Eid al-Fiṭr and Eid al-Aḍḥā—then deliver the sermon, putting the prayer before the sermon.
Thus this narration establishes that the prayer precedes both Eid sermons; the remaining rulings will come in the reports that follow.

Hadith Two
Al-Barāʾ ibn ʿĀzib (may Allah be pleased with him) reported:
The Prophet ﷺ addressed us on the Day of Sacrifice after the prayer and said, “Whoever performs our prayer and offers the sacrifice as we do has attained the prescribed rite; but whoever slaughters before the prayer has no sacrifice.”

Abū Burdah ibn Niyār—the maternal uncle of al-Barāʾ—said, “Messenger of Allah, I slaughtered my sheep before the prayer. I knew today is a day of eating and drinking, and I wanted my animal to be the first slaughtered in my household, so I killed my sheep and ate breakfast before coming to the prayer.” He ﷺ replied, “Your sheep is just meat.”

Abū Burdah then said, “Messenger of Allah, we have a she-kid that is dearer to us than two sheep. Would it count for me?” He ﷺ said, “Yes, but it will not suffice for anyone after you.”

Glossary of hadith terms:
• nusuk (ritual slaughter): the act of sacrificing; nuskah means “a sacrificed animal.” In other, figurative contexts the word carries additional meanings, but here it refers to the slaughter just mentioned. The plural of nuskah is nusuk with the sīn vocalised; when the sīn is silent the term denotes ‘worship’ in general.
• ʿanāq: a female kid of the goats that has grown strong but has not yet completed one lunar year (pronounced with an open ʿayn and light nūn).

Overall meaning of the hadith:
On the morning of Eid al-Aḍḥā, after completing the prayer, the Prophet ﷺ explained the rulings and the proper time for slaughter on that day. He clarified that whoever performs the Eid prayer as he did and sacrifices in the same manner has fulfilled the prescribed rite. Anyone who slaughters before the Eid prayer does so outside the appointed time; his animal counts merely as ordinary meat, not as an accepted sacrifice.

When Abū Burdah heard the Prophet’s khutbah he said, “Messenger of Allah, I sacrificed my sheep before the prayer. Knowing that today is for eating and drinking, I wished my animal to be the first slaughtered in my household, so I killed it and ate before coming to the prayer.”

The Prophet ﷺ replied, “Your slaughter is not a valid sacrificial rite; it is only meat.”