صلى الله عليه وسلم
Ṣallā Allāhu ʿalayhi wa sallam
May God bless him and grant him peace: said after the name of the Prophet Muhammad or when he is called the Prophet of God.
What it means
The phrase ṣallā Allāhu ʿalayhi wa sallam means “may God send blessings and peace upon him”. Muslims say or write it every time they mention the Prophet Muhammad (peace be upon him), and also when they call him the Prophet of God. In English texts it is often given as “peace be upon him”. The Quran gives the basis: “God and His angels send blessings upon the Prophet. O you who believe, send blessings upon him and greet him with peace” (33:56). The practice shows love and respect for the one who brought the message. Faruqi lists it among the expressions that are said in Arabic and not replaced by a vague English equivalent.
Often misunderstood as
The abbreviations SAW and PBUH can read as bare labels, whereas the phrase is a full invocation to God for blessing and peace upon the Prophet.
What the sources say
The Prophet Muhammad (peace be upon him) said that whoever sends one blessing upon him, God sends ten upon that person (Sahih Muslim). Scholars therefore encourage Muslims to say the phrase in full whenever they mention him, in speech and in writing.
Term and Arabic as listed in Ismail al Faruqi, Toward Islamic English (International Institute of Islamic Thought, 1995), p. 58, listed as ṢALLĀ ALLAHU ‘ALAYHI WA SALLAM.. The definition is restated here.