MAQAM E IBRAHIM
Maqam - e - Ibrahim is the stepping stone used by Prophet Ibrahim (Peace be upon him) during the original construction of the Ka`bah. The stone carries the imprints of his feet and is housed in a glass enclosure on the north side of the Ka`bah. The footprints of al-Khaleel (Ibraaheem, Peace be upon him) remained on the rock until the beginning of Islam. Al-Bidaayah wa’l-Nihaayah, 1/163 
Once the Tawaaf is completed, the haaji or pilgrim should head towards the Muqam-e-Ibrahim (Place of Ibrahim). It is good to pray 2 rak’ah behind Maqam e Ibrahim, if possible.
Muqam-Ibrahim (Place of Ibrahim) is a small yet round shaped building sort of structure while lies in the front of the door of the Kaaba and the Multazam. This structure has actually a stone which has been present in its place since the time of Ibrahim. It was the stone used by Ibrahim in the construction process that is why it is called Muqam-Ibrahim (Place of Ibrahim). Once the seventh round is completed of Tawaaf during the Hajj, two raka’at of prayers are offered at this place.
In order to complete the upper part of the walls of the Kaaba, Ibrahim stood upon a large stone block which he moved along when each section was completed. When the Kaba was finished, the large stone block was left outside the Kaaba, close to the eastern wall of the sanctuary. It became known as the Maqam Ibrahim (the station of Ibrahim). Today, the Maqam Ibrahim (Alaihi salam), with the stone within, is located in front of the door of the Kaaba. The boulder is about 2 x 3 feet. Where it stands today is the place where Ibrahim offered up his prayers.
Indeed, the first House [of worship] established for mankind was that at Bakkah (Original name of 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.Qur’an.Surah A’le Imran 3:96-97
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]." Qur’an.Surah Baqrah 2:125 
Each year nearly several million people make the pilgrimage, making it the largest temporary gathering on the globe. It is an act of recollection and worship, but also a symbolic act representing the spirit's return to its homeland-one of the central elements of the Muslim life. Hajj is an imperative duty (fardh) for all Muslims physically and financially able to perform it.
The rites begin and end at the Ka'ba the square 'House' built as we Muslims believe, by Adam (peace be upon him)and restored by Ibrahim ((peace be upon him) and his elder son Ismael (peace be upon him).
It is not obligatory to perform two Rak`ahs behind Maqam Ibrahim. It will be sufficient to perform them at any place in Al-Haram (the Sacred Mosque in Makkah). But there will be no blame on a person who forgets them because they are supererogatory acts of worship, but not an obligation. (Fatawa by Shaykh Ibn Baaz )
A person can move away from the place where people are doing Tawaaf and pray two rak’ahs. Even Ameer al-Mu’mineen ‘Umar ibn al-Khattaab (R) prayed the two rak’ahs of tawaaf in Dhu Tuwa, which is far away from al-Masjid al-Haraam, and is not even in al-Masjid al-Haraam. 
Shaykh Ibn ‘Uthaymeen (May Allah have mercy on him) said:
Undoubtedly Maqaam Ibrahim is proven and that on which the glass enclosure is built is indeed Maqaam Ibrahim. But the engraved marks that appear on it do not seem to be footprints, because what is well known from an historical point of view is that those footprints disappeared a long time ago. But these engraved marks were meant as a marker only, and we cannot be certain that these are the footprints of Ibrahim (peace be upon him).