why we call it ibrahimic prayer ?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The Ibraaheemic prayer is called by this name because in it we exalt the mention of Prophet Ibraaheem (Abraham) .

As regards why the Prophet Ibraaheem was especially given that, then it is because he and his family had achieved many multiplied traits, so Allaah expanded His Mercy and Blessings over him; Allaah Says (what means): {May the mercy of Allaah and His blessings be upon you, people of the house. Indeed, He is Praiseworthy and Honorable.”}[Quran 11:73]

Therefore, it was suitable to supplicate for the Prophet with such supplication so that the same good that is given to the Prophet Ibraaheem and to his family will be given to him.

The Ibraaheemic prayer is for a Muslim to say:

“Allaahumma salli `ala Muhammad wa `ala `aali Muhammad kama sallayta `ala Ibraaheem wa `ala `aali Ibraaheem Innaka Hameed-un-Majeed. Allaahumma baarik `ala Muhammad wa `ala `aali Muhammad kama baarakta `ala Ibraaheem wa `ala `aali Ibraaheem Innaka Hameed-un-Majeed.” [O Allaah exalt Muhammad and the followers of Muhammad, just as You had exalted the family of Ibraaheem.  Verily, You are full of Praise and Majesty. O Allaah, send blessings upon Mohammad and upon the family of Muhammad, just as You had sent blessings upon the family of Ibraaheem.  Verily, You are full of Praise and Majesty.][Al-Bukhari and Muslim]

Indeed, there are other forms of exaltations but this is the form which is narrated by Al-Bukhari and Muslim .

Allaah Knows best.