1 And David said, "Is there yet anyone who is left of the house of Saul so that I may show him kindness for Jonathan's sake?" 2 And there was of the house of Saul a servant whose name was Ziba. And when they had called him to David, the king said to him, "Are you Ziba?" And he said, "Your servant is he." 3 And the king said, "Is there not yet any of the house of Saul so that I may show the kindness of God to him?" And Ziba said to the king, "Jonathan has yet a son who is lame in his feet." 4 And the king said to him, "Where is he?" And Ziba said to the king, "Behold, he is in the house of Machir, the son of Ammiel, in Lo-debar." 5 Then king David sent and brought him from the house of Machir, the son of Ammiel, from Lo-debar. 6 Now when Mephibosheth, the son of Jonathan, the son of Saul, had come to David, he fell on his face and did reverence. And David said, "Mephibosheth." And he answered, "Behold your servant!" 7 And David said to him, "Do not fear, for I will surely show you kindness for the sake of Jonathan your father and will restore you all the land of Saul your father, and you shall eat bread at my table continually." 8 And he bowed himself and said, "What is your servant that you should look upon such a dead dog as I am?"
9 Then the king called to Ziba, Saul's servant, and said to him, "I have given to your master's son all that pertained to Saul, and to all his house. 10 Therefore, you, your sons, and your servants shall till the land for him, and you shall bring in the fruits so that your master's son may have food to eat. But Mephibosheth your master's son shall always eat bread at my table." Now Ziba had fifteen sons and twenty servants. 11 Then Ziba said to the king, "According to all that my lord the king has commanded his servant, so your servant shall do." "As for Mephibosheth," the king said, "he shall eat at my table as one of the king's sons." 12 And Mephibosheth had a young son whose name was Micah. And all who dwelt in the house of Ziba were servants to Mephibosheth. 13 So Mephibosheth dwelt in Jerusalem, for he ate continually at the king's table. And he was lame in both his feet.
[v.3] - "Jonathan has yet a son, who is lame in his feet" - Reference, 2nd Samuel 4:4.
[v.8] - Mephibosheth's response is very similar to the response David gave to God in Psalm 8:4, which says, "What is man, that you are mindful of him, and the son of man, that you visit him?" This is a show of reverence in the presence of a king--Mephibosheth before David, and David before God. This should also be the response of every Christian: 1) to Christ for the price He payed on the cross, and 2) to God the Father for sending His Son to die as an act of grace.
[v.11] - "he shall eat at my table, as one of the king's sons" - This is an act of grace towards Mephibosheth on behalf of David. Mephibosheth, being lame in his feet and therefore deemed unfit to receive the kingdom, would probably have lived a life of either poverty or basic living. David seeks him out and desires to show him kindness by restoring to him the land of his father, which would give him status in society, and allow him to eat at his table. This very act parallels the way God redeems His elect. He seeks out His chosen among sinners, who are dead in their sins, and restores to them their inheritance in the kingdom of Heaven, all as an act of grace (Ephesians 1:3-14, 2:2, 8).