In the verses leading up to this week's lesson from 1 Kings, Elijah is fleeing for his life. In frustrating despair, he compares his efforts with the poor results he has achieved. Looking back, Elijah sees his zealousness for the Lord and no zealousness on the part of the Israelites. He says to the Lord, "They have forsaken your covenant, thrown down your altars, and killed your prophets."
Elijah feels that he is alone without any support.
The Lord gives him more work to do: Anoint a king to replace Ahab. Anoint a prophet to continue your work.
Elijah continues his journey. He finds Elisha, the one the Lord has designated to be his successor.
Elisha is at work plowing when Elijah approaches him. He's ready to go but wants to say goodbye to his parents first. Commentators disagree on whether the text tells us that Elijah let him do this or not. In either case, Elisha slaughtered the oxen providing a meal to feed the people. Then he set out with Elijah.