Allah says,
Indeed, the first House [of worship] established for mankind was that at Makkah - blessed and a guidance for the worlds.
In it are clear signs [such as] the standing place of Abraham. And whoever enters it shall be safe. And [due] to Allah from the people is a pilgrimage to the House - for whoever is able to find thereto a way. But whoever disbelieves - then indeed, Allah is free from need of the worlds.
[Aal-Imraan: 96-97]

Maqam Ibraheem is the stone on which Ibraheem stood while building the higher walls of the Ka'bah. This stone has the footprints of Ibraheem .

Abdullah bin Amr narrated that :
He heard the Messenger of Allah saying: "Indeed the Corner and the Maqam are two corundums from the corundum of Paradise. Allah removed their lights, and if their lights had not been removed then they would illuminate what is between east and the west." [Tirmidhi]

Literally 'maqam' means station as in high place and dignified rank. Prophets Ibrahim and Ismail (peace be upon them) together built the Kaaba. To reach the top of the Kaaba, Prophet Ibrahim stood on a large rock and his feet left their prints, bearing witness of his great deed for all time. And it is there at Maqam Ibrahim that the father and son, Prophets Ibrahim and Ismail, are believed to have prayed after building the Kaaba.

The rock itself is on a base of stone built over 20cm of marble that stands in the ground. The actual footprints of Prophet Ibrahim's are of an oval rectangular shape and have been entirely plated in silver. Because of the passing of time, its colors vary between shades of white, black and yellow. A dome was first placed over Maqam Ibrahim in 810 H and it has been rebuilt at intervals.

During Hazrat Umar bin Al-Khattab’s (R.A) reign, he shifted the place and moved the Maqam more towards the east, so that the individuals who try to perform Tawaaf are able to perform it conveniently, without being in the way for individuals who pray after completing their Tawaaf next to Maqam-e-Ibrahim.

Allah says,
And [mention] when We made the House a place of return for the people and [a place of] security. And take, [O believers], from the standing place of Abraham a place of prayer. And We charged Abraham and Ishmael, [saying], "Purify My House for those who perform Tawaf and those who are staying [there] for worship and those who bow and prostrate [in prayer]." [Al-Baqarah: 125]

Narrated `Umar (bin Al-Khattab) :
My Lord agreed with me in three things:
-1. I said, "O Allah's Messenger (ﷺ), I wish we took the station of Abraham as our praying place (for some of our prayers). So came the Divine Inspiration: And take you (people) the station of Abraham as a place of prayer (for some of your prayers e.g. two rak`at of Tawaf of Ka`ba)". (2.125)
-2. And as regards the (verse of) the veiling of the women, I said, 'O Allah's Messenger (ﷺ)! I wish you ordered your wives to cover themselves from the men because good and bad ones talk to them.' So the verse of the veiling of the women was revealed.
-3. Once the wives of the Prophet (ﷺ) made a united front against the Prophet (ﷺ) and I said to them, 'It may be if he (the Prophet) divorced you, (all) that his Lord (Allah) will give him instead of you wives better than you.' So this verse (the same as I had said) was revealed." (66.5). [Bukhari]