Nephi’s large stature and strength are essential to restrain the servant, who would certainly have been extremely scared and attempting to flee. Realizing that Nephi must have killed Laban in order to be wearing his clothes and carrying his sword, it was a small step to suppose that Nephi might also kill him.
To comfort him, Nephi swears an oath, and the situation appears to change immediately. The power of an oath in the ancient world was similar to a contract in the modern world. Depending upon how the oath was sworn, the servant would understand that he would not be killed. He listened to his options.
Nephi offers the servant the chance to change his effective social status. Although he had served a wealthy man in Jerusalem, he was still a servant. Freedom would be an important incentive. Secondly, Nephi offers him a place in Lehi’s family. This was an informal adoption, a promise of familial protection. He would share in the protection of the family. Nephi was confirming that they did not take him to some point far from Jerusalem and then set him free to fend for himself among strangers.