Muhammed Mustafa, the Messenger of Allah, shared all the sorrows and afflictions of his followers who were being tortured for believing in Tauheed but he had no means to protect them. When it appeared that there was going to be no deescalation in the violence against and persecution of the Muslims by the pagans, he suggested to them to leave Makka, and to seek sanctuary in Abyssinia which was then ruled by a Christian king, well-known for being a just and a God-fearing man.
Following this suggestion, a group of Muslims, comprising eleven men and four women, left Makka and went to Abyssinia. The group included Uthman bin Affan, a future khalifa of the Muslims, and Zubayr bin al-Awwam, a cousin of the Prophet. The Prophet appointed one of his principal companions, Uthman bin Mazoon, as the leader of this group.

Muhammad ibn Ishaq

When the Apostle saw the afflictions of his companions and that though he escaped them because of his standing with Allah and his uncle, Abu Talib, he could not protect them, he said to them: "If you were to go to Abyssinia (it would be better for you), for the king (there) will not tolerate injustice and it is a friendly country, until such time as Allah shall relieve you from distress." Thereupon his companions went to Abyssinia, being afraid of apostasy and fleeing to God with their religion. This was the first hijra in Islam.
(The Life of the Messenger of God)
The first migration took place in the fifth year of the Call (Proclamation), i.e., in AD. 615.
The king of Abyssinia welcomed the Muslim refugees from Makka into his kingdom. He gave them sanctuary, and they found peace and security, and they enjoyed freedom of worship.

It is reported that about a year later, the Muslim refugees in Abyssinia heard rumors that the Quraysh in Makka had accepted Islam. If it was so, then there was no reason for them to live in exile, and they were very homesick. They, therefore, returned to Makka. But in Makka they found out that not only the reports of the conversion of the Quraysh to Islam were false but also that the latter had stepped up the persecution of the Muslims. They, therefore, left Makka once again but not alone. Many other Muslims accompanied them to Abyssinia. This new group comprised 83 men and 18 women, and may have included both the old and the new emigrants; among them were Abdur Rahman ibn Auf, Abu Salma Makhzoomi, and Abdullah ibn Masood. Muhammed Mustafa, the Messenger of Allah, appointed his cousin, Jaafer ibn Abi Talib, the elder brother of Ali, as the leader of this group.
The second migration of the Muslims to Abyssinia took place in the sixth year of the Call (Proclamation), which corresponds to A.D. 616.
The migration of the Muslims, and their reception in Abyssinia, alarmed the Quraysh of Makka. They entertained the fear that the Muslims in Abyssinia might grow in strength or might find new allies, and then, some day, might return to Makka to challenge them. Therefore, to head off this potential threat, such as they saw it, they decided to send an embassy to the court of the king of Abyssinia to request him to extradite the Muslims to Makka.
The Muslim refugees who had expected to be left in peace, were surprised and dismayed by the arrival, in the Abyssinian capital, of an embassy from Makka, led by a certain Amr bin Ass. Amr had brought rich presents for the king and his courtiers to ingratiate himself with them.
When the king gave audience to the emissary of the Quraysh, he said that the Muslims in Abyssinia were not refugees from persecution but were fugitives from justice and law; and requested him to extradite them to Makka. The king, however, wanted to hear the other side of the story also before giving any judgment, and summoned Jaafer ibn Abi Talib, the leader of the refugees, to answer the charges against the Muslims.

Jaafer made a most memorable defence. Following is a summary of his speech in the Abyssinian court in reply to the questions posed by the Christian king.
"O king! We were ignorant people and we lived like wild animals. The strong among us lived by preying upon the weak. We obeyed no law and we acknowledged no authority save that of brute force. We worshipped idols made of stone or wood, and we knew nothing of the human dignity. Then God in His mercy sent to us His messenger who was himself one of us. We knew about his truthfulness and his integrity. His character was exemplary, and he was the most well-born of the Arabs. He forbade us to worship idols and he invited us to the worship of One God. He exhorted us to speak the truth, and to protect the weak, the poor, the humble, the widows and the orphans. He ordered us to show respect to women, and never to slander them. We obeyed him and followed his teachings. Most of the people in our country are still polytheists, and they resented our conversion to the new faith. They began to persecute us, and it was in order
to escape from persecution by them that we sought and found sanctuary in your kingdom."
When Jaafer concluded his speech, the king declared that he was convinced of his veracity, and added, to the great disappointment of Amr bin Ass, that the Muslims could live in his kingdom as long as they wished, without any fear.
But Amr bin Ass bethought himself of a new argument which, he felt confident, would appeal to the king who was a Christian. If it did, he was certain, it would tilt the scales against the Muslims, and they would be extradited.
On the following day, therefore, he returned to the court and said to the king that he (the king) ought to waive his protection of the Muslims because they rejected the divine nature of Jesus, and asserted that he was a mortal like other men. When questioned on this point by the king, Jaafer said: "Our judgment of Jesus is what was revealed to our Prophet, viz., that Jesus is the servant of God, and is His Prophet, His Spirit, and His Command given unto Mary, the innocent virgin."
The king said to Jaafer: "Jesus is just what you have stated him to be, and is nothing more than that." Then turning toward the Muslims, he said: "Go to your homes and live in peace. I shall never give you up to your enemies." He refused to extradite the Muslims, returned the presents which Amr bin Ass had brought, and dismissed his embassy.

Washington Irving

"Among the refugees to Abyssinia, there was Jaafer, the son of Abu Talib, and brother of Ali, consequently the cousin of Mohammed. He was a man of persuasive eloquence and a most prepossessing appearance. He stood forth before the king of Abyssinia, and expounded the doctrines of Islam with zeal and power. The king who was a Nestorian Christian,
found these doctrines so similar in many respects to those of his sect and so opposed to the gross idolatry of the Koreishites, that so far from giving up the fugitives, he took them more especially into favor and protection, and returning to Amr b. Ass and Abdullah, the presents they had brought, dismissed them from his court."
(The Life of Mohammed)