Hadith: The Prophet (may Allah's peace and blessings be upon him) delivered a sermon after having offered the prayer on Eid al-Ad'ha. He said: Whoever prayed our prayer and slaughtered our sacrifice has properly observed the ritual. And whoever slaughtered (his sacrifice) before the (Eid) prayer has not observed the ritual

عن البَرَاء بن عَازب رضي الله عنهما قال: «خطبنا النبي صلى الله عليه وسلم يوم الأضحى بعد الصلاة، فقال: من صلى صلاتنا وَنَسَكَ نُسُكَنَا فقد أصاب النُّسُكَ، ومن نسك قبل الصلاة فلا نُسُك له. فقال أبو بُرْدَةَ بن نِيَار -خال البَرَاء بن عَازبٍ-: يا رسول الله، إني نسكت شاتي قبل الصلاة، وعرفت أن اليوم يوم أكل وشرب، وأحببت أن تكون شاتي أول ما يذبح في بيتي، فذبحت شاتي، وتغديت قبل أن آتي الصلاة. فقال: شاتك شاة لحم. قال: يا رسول الله، فإن عندنا عَنَاقًا لنا هي أحب إلي من شاتين؛ أَفَتَجْزِي عني؟ قال: نعم، ولن تَجْزِيَ عن أحد بعدك».
[صحيح] - [متفق عليه]

Al-Barā' ibn ‘Āzib (may Allah be pleased with him) reported: The Prophet (may Allah's peace and blessings be upon him) delivered a sermon after having offered the prayer on Eid al-Ad'ha. He said: "Whoever prayed our prayer and slaughtered our sacrifice has properly observed the ritual. And whoever slaughtered (his sacrifice) before the (Eid) prayer has not observed the ritual." Abu Burdah ibn Niyār (the uncle of Al-Barā' ibn ‘Āzib) said: "O Messenger of Allah, I slaughtered my sheep before the prayer. I know that today is a day of eating and drinking, so I liked to have my sheep as the first thing to be slaughtered at my home. I slaughtered it and ate before coming to the prayer." The Prophet (may Allah's peace and blessings be upon him) replied: "The sheep which you have slaughtered is just a sheep (slaughtered) for meat (i.e. not a ritual sacrifice)." He (Abu Burdah) said: "O Messenger of Allah, we have a young she-goat which is dearer to me than two sheep. Will that be valid as a sacrifice for me?" The Prophet (may Allah's peace and blessings be upon him) said: "Yes, but it will not be valid (as a sacrifice) for anyone else after you."
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

The Prophet (may Allah's peace and blessings be upon him) delivered a sermon on the Day of Eid al-Ad'ha after having offered the prayer. He explained the rulings of slaughtering and its prescribed time on the day of Eid to the Companions. He added that whoever offered prayer and sacrificed in the same manner as the Prophet (may Allah's peace and blessings be upon him) did, his ritual would be properly observed. However, if someone slaughtered his animal before the prescribed time of slaughtering started, then his sacrifice would be considered normal slaughtering for the sake of meat, and not an accepted rite or act of worship. When Abu Burdah heard this, he asked: "O Messenger of Allah, I slaughtered my sheep before the prayer. I know that today is a day of eating and drinking, so I liked to have my sheep as the first thing to be slaughtered at my home. I slaughtered it and ate before coming to the prayer." The Prophet (may Allah's peace and blessings be upon him) told him that this was not the prescribed sacrifice and that it would be considered as an animal slaughtered to make use of its meat only. Abu Burdah then told the Prophet that he had a young she-goat which was dearer to him than two sheep; and he asked if slaughtering it would be considered a valid sacrifice for the sake of Allah? The Prophet (may Allah's peace and blessings be upon him) said: Yes, but this ruling is for you exclusively and is not generalized for the rest of the Ummah, as a little she-goat is not valid for sacrifice until it has completed one year of age.