Hadith 695
Anas (May Allah be pleased with him) reported:
عن أنس رضي الله عنه أن النبى صلى الله عليه وسلم كان إذا تكلم بكلمة أعادها ثلاثاً حتى تفهم عنه، وإذا أتى على قومٍ فسلم عليهم سلم عليهم ثلاثاً. ((رواه البخاري)).
Whenever the Prophet (ﷺ) said something, he would repeat his words thrice so that the meanings would be understood fully; and whenever he came upon a group of people, he would greet them, and he would repeat salutation thrice. [Al-Bukhari].
In plain words
The Prophet would repeat his words three times so their meaning was fully grasped, and would repeat his greeting three times to a group. Patient repetition helped people truly understand.
Reference : Riyad as-Salihin 695 In-book reference : Book 1, Hadith 16