Jamrat is a Hajj ritual that involves stoning the three pillars that represent the devil (shaytan in Arabic). As part of this Hajj ritual, the pilgrims throw small pebbles at those three structures of Jamrat in the city of Mina. Pilgrims collect these pebbles at Muzadlifah. These pebbles (small stones) can also be collected in the city of Mina, east of Makkah. The process of casting or stoning of seven pebbles to these pillars is called as Rami or Ramee.
Stoning the Jamaraat is one of the obligatory rituals of Hajj and is prescribed for everyone who intends to do this great pilgrimage. This ritual is mentioned clearly in the Sunnah and its authenticity is agreed upon by the scholars.
The historical significance of Jamrat ritual hails from Prophet Ibraheem when the devil appeared to him three times. At each of the appearances, Angel Jibraeel (Gabriel) told Prophet Ibraheem (Abraham) to pelt the devil. Thus, the basis of the significance of the ritual.  
It was narrated from Ibn ‘Abbaas (may Allaah be pleased with him) that the Prophet ﷺseated al-Fadl behind him on his mount, and al-Fadl said that he did not stop reciting the Talbiyah until he stoned the Jamrah. Sahih al-Bukhari 1685 and Sahih Muslim 1282
It was narrated from ‘Abd-Allaah (may Allaah be pleased with him) that he came to the largest Jamrah and put the House on his left and Mina on his right and stoned it with seven (pebbles), and he said: This is how the one to whom Soorat al-Baqarah was revealed ﷺstoned it. Sahih al-Bukhari 1748 and Sahih Muslim 1296
It was narrated from Ibn ‘Umar (may Allaah be pleased with him) that he would stone al-Jamrah al-Dunya (the Jamrah near the Khaif mosque) with seven pebbles, saying takbeer after every throw. Then he would go ahead until he reached the level ground where he would stand facing the qiblah, and he stood for a long time, offering du’aa’ and raising his hands. Then he would stone the middle pillar, then he would move to the left towards the middle ground, where he would stand facing the qiblah. He would remain there for a long time offering du’aa’ and raising his hands. Then he would stone Jamrat al-‘Aqabah from the middle of the valley, but he did not stand beside it. Then he would leave and say: This is how I saw the Prophet ﷺdoing it. Sahih al-Bukhari 1751
The first (minor) pillar called as Jamra e Ulaa (Sughra) is close to the Al-Khaif Mosque, 155 meters from the first pillar is the second (medium) pillar(Jamra e Wusta). The third (major) pillar, another 155 meters on, is known as the pillar of Aqabah (Jamra e Uqbah or Kubra). Pilgrims start the stoning with the minor pillar and then move on to the medium pillar and the major pillar. 
Ibn al-Mundhir (may Allaah be pleased with him) said: They were unanimously agreed that if a person stones the Jamaraat during the days of al-Tashreeq after the sun has passed the meridian, that is valid. AL-IJMAA’ BY IBN AL-MUNDHIR (11)
Ibn Hazm (may Allaah be pleased with him) said: They agreed that the three days after the Day of Sacrifice are the days for stoning the Jamaraat, and that the one who stoned them during those days after the meridian, that is valid. MARAATIB AL-IJMAA’ BY IBN HAZM (46)
Ibn Qudaamah (may Allaah have mercy on him) said: When he reaches Mina, he should start with Jamrat al-‘Aqabah, which is the furthest of the Jamaraat from Mina and the closest of them to Makkah, and it is at al-‘Aqabah, hence it is also called Jamrat al-‘Aqabah. He should stone it with seven pebbles, saying takbeer with each throw. He should stand at the middle of the valley and turn to face the qiblah, then he should leave and should not stay there. This is a summary of the views of those scholars whose views we know. Al-Mughni (3/218) 
There are many mistakes committed by some pilgrims when stoning the Jamaraat.
  http://islamqa.info/en/125711