Alaihi is a prepositional phrase meaning "Upon him." It is most commonly used in the "Salavat" or "Taslim" after the name of a Prophet: "Alaihi al-Salam" (Peace be upon him). For the Prophet Muhammad (PBUH), we say "Sallallahu Alaihi wa Sallam." This is an act of "Ibadah" (worship) and "Hubb" (love) that fulfills a Quranic command (33:56). Sending "Salam" upon the Prophets connects the believer to the "Silsila" (chain) of Divine guidance. The Prophet (PBUH) said that for every "Salavat" we send, Allah sends ten blessings upon us, making "Alaihi" a key to "Barakah" (blessing) and Divine mercy.