Hadith: Verily Allah sent Muhammad (may Allah's peace and blessings be upon him) with the truth and sent the Book down to him. Part of what was revealed to him was the verse on stoning. We recited, understood, and comprehended it. The Messenger of Allah (may Allah’s peace and blessings be upon him) did administer stoning and we administered it after his death

عن عبد الله بن عباس رضي الله عنهما أن عمر بن الخطاب رضي الله عنه قال وهو جالس على منبر رسول الله صلى الله عليه وسلم : "إن الله قد بعث محمدًا صلى الله عليه وسلم بالحق، وأنزل عليه الكتاب، فكان مما أُنْزِلَ عليه آية الرجم، قَرَأْنَاَهَا وَوَعَيْنَاَهَا وعَقِلْنَاَهَا، فَرَجَمَ رسول الله صلى الله عليه وسلم ، ورجمنا بعده، فأخشى إن طال بالناس زمان أن يقول قائل: ما نجد الرجم في كتاب الله فَيَضِلُّوا بترك فريضة أنزلها الله، وإن الرجم في كتاب الله حَقٌّ على من زنى إذا أَحْصَنَ من الرجال والنساء، إذا قامت البينة، أو كان الحَبَلُ، أو الاعتراف".
[صحيح] - [متفق عليه]

‘Abdullāh ibn ‘Abbās reported that ‘Umar ibn al-Khattāb, while he was sitting on the Prophet's pulpit, said: "Verily Allah sent Muhammad (may Allah's peace and blessings be upon him) with the truth and sent the Book down to him. Part of what was revealed to him was the verse on stoning. We recited, understood, and comprehended it. The Messenger of Allah (may Allah’s peace and blessings be upon him) did administer stoning and we administered it after his death. Yet, I am concerned that, after a long time has passed, someone may say: 'We cannot find stoning in Allah's Book,' and they will be led astray for abandoning an obligation that Allah has sent down. Indeed, stoning is established in the Book of Allah against those married men and women who commit adultery, when there is evidence, pregnancy, or a confession."
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

‘Umar ibn al-Khattāb (may Allah be pleased with him) got up onto the pulpit and delivered a sermon to people. He said: among other things, that Allah had sent Muhammad (may Allah's peace and blessings be upon him) with the true religion; Islam, and He had sent the best Book; the Qur’an, down to him. Included in what was sent down was the verse on stoning a married person who commits adultery. The wording of the verse was abrogated, but its ruling remained. ‘Umar (may Allah be pleased with him) feared that people of later times who had not witnessed the revelation of the Qur’an would deny the stoning ruling. So he reminded people of the ruling and that it was true. Therefore, if a legally married person is found committing adultery, confesses and admits to it; or if a married woman gets pregnant in the absence of her husband or master (in the case of a slave woman), she should be stoned to death. These are the proofs that can be used to establish the punishment of stoning for a person who has committed adultery.