Hadith: Whenever the Prophet (may Allah's peace and blessings be upon him) spoke a word, he would repeat it thrice until it is understood from him. Whenever he greeted a group of people, he would greet them thrice

عن أنس بن مالك رضي الله عنه أَنَّ النَبيَّ -صلَّى الله عليه وسلَّم- كَان إِذَا تَكَلَّمَ بِكَلِمَةٍ أَعَادَهَا ثَلاَثًا حَتَّى تُفْهَمَ عَنْهُ، وَإِذَا أَتَى عَلَى قَوْمٍ فَسَلَّمَ عَلَيهِم سَلَّمَ عَلَيهِم ثَلاَثًا.
[صحيح] - [رواه البخاري]

Anas ibn Mālik (may Allah be pleased with him) reported: Whenever the Prophet (may Allah's peace and blessings be upon him) spoke a word, he would repeat it thrice until it is understood from him. Whenever he greeted a group of people, he would greet them thrice.
[Authentic hadith] - [Narrated by Bukhari]

Explanation

According to the Hadīth reported by Anas ibn Mālik (may Allah be pleased with him), whenever the Prophet (may Allah's peace and blessings be upon him) spoke a word, he would repeat it three times to be understood. "Until it is understood from him" indicates that if the speech is understood without repetition, then he would not repeat it. However, if a person cannot understand what is said: like when there is someone who does not know the meaning properly, or one who has deficient hearing, or there is much noise, then it is recommended for the speaker to repeat his words until he is understood properly. Moreover, whenever he greeted a group of people "he would greet them thrice," i.e. he did not repeat it more than thrice. He would extend the greeting once, and if it was not returned he would repeat it. If it was not returned, he would extend it for a third and last time. Likewise, when seeking permission to enter, he would seek it thrice, i.e. when he came to visit someone he would knock at the door thrice. If no one answered, he would leave. This the Sunnah of the Prophet (may Allah's peace and blessings be upon him) to repeat things thrice then stop.