The meaning of sending blessings upon the Prophet
“Allaahumma salli ‘ala Muhammad wa ‘ala Aali Muhammad kama salayta ‘ala aali Ibraaheem, wa baarik ‘ala Muhammad wa ‘ala aali Muhammad kama baarakta ‘ala aali Ibraaheem innaka hameedun majeed (O Allaah, send prayers upon Muhammad and upon the family of Muhammad as You sent prayers upon the family of Ibraaheem, and send blessings upon Muhammad and upon the family of Muhammad, as You sent blessings upon the family of Ibraaheem, You are indeed Worthy of Praise, Full of Glory).”
“Allaahumma” means, O Allaah.
“Salli ‘ala Muhammad (send prayers upon Muhammad).” The prayers of Allaah upon Muhammad means His praising him before the higher assembly, i.e., the angels who are close to Him.
“Wa ‘ala aali Muhammad (and upon the family of Muhammad)” means and send blessings upon the family of Muhammad. It was said that the family of Muhammad are his followers who follow his religion; or it was said that the family of the Prophet (peace and blessings of Allaah be upon him) are his relatives who believed. The first view is the one which is correct because the word “aal” (translated here as “family”) means followers.
“Kama salayta ‘ala Ibraaheem (as You sent prayers upon the family of Ibraheem).” Some of the scholars said that what this means is: as You previously bestowed Your bounty upon the family of Ibraaheem, then bestow Your bounty upon Muhammad and His family.
“Baarik ‘ala Muhammad wa ‘ala aali Muhammad (Send blessings upon Muhammad and upon the family of Muhammad)” means send down blessings. Blessings means a lot of good things on a continuous and ongoing basis.
“Kama baarakta ‘ala aali Ibraaheem (as You sent blessings upon the family of Ibraaheem)” i.e., O Lord, You bestowed Your favour upon the family of Ibraaheem and blessed them, so send blessings upon the family of Muhammad.
“Innaka hameedun majeed (You are indeed Worthy of Praise, Full of Glory). Hameed means praising and praiseworthy, praising His slaves and close friends who obey His commands, and praiseworthy, to be praised for His attributes of perfection and great blessings.
Majeed means Owner of Majesty. Majesty means greatness and perfect power.
Al-Sharh al-Mumti’, 3/227.