The acronym “PBUH” stands for “Peace Be Upon Him”. We Muslims say “Peace be upon him” in order to bless and honor Muhammad pbuh, just as the abbreviation “SAW” Sallallah ho Alaihe wa aali hi Wasallam (صلى الله عليه وسلم) for the corresponding Arabic expression. It is not mandatory but it is so recommended and this verse of the Quran could be mentioned as the evidence of this recommendation:
“Indeed Allah and His angels bless the Prophet; O you who have faith! Invoke blessings on him and invoke Peace upon him in a worthy manner”. (33 :56)
If we examine the grammar of the Arabic words, we find it’s a statement not a request (or supplication). So, the term is a type of a “title” as a mark of respect, which means “Allah’s Blessings and Peace are on him”. However, God has also kept an element of invoking blessings upon the Prophets. It also includes all the righteous followers along with the Prophets. It is counted as a good deed. It also serves a purpose of maintaining our connection and reminding us of the Prophet (his ways), so that we may follow him better. Along with this, including all the followers, creates a feeling of brotherhood and harmony and also, in a way, makes us more righteous and motivated.
God’s blessings are always upon His pious messengers, no matter what. Invoking blessings upon them is an act of reward for us, an act of worship (or obedience) because we are fulfilling one instruction of our Lord. Furthermore, this act is also beneficial for us in many other ways too, and moreover it gives us the feeling of belonging to one Ummah. Acronym pbuh is just a verbal, or textual proclamation which manifests our sincerity, love, and respect for our beloved Prophet Muhammad PBUH which lies in our heart.