In this chapter, David provides for the welfare of Mephibosheth.
This is another short and relatively uneventful chapter. Basically, there are two things happening in this chapter. The first (and overt) objective is that David wants to "show kindness" to one of the descendants of Saul for the sake of his promise to Jonathan, which David made in 1 Samuel 20:15.
So David restores all of Saul's land (probably referring to the land of his inheritance, plus whatever land he had bought) to Mephibosheth, as Mephibosheth appears to have been taken into hiding when his uncle, Ish-Bosheth, was fighting a war against David. David also promises to let Mephibosheth eat free meals from the king's table.
A second, less obvious purpose for David's action in doing this is to keep Mephibosheth near Jerusalem, where he can be more easily monitored. Although he certainly seems helpless now, Mephibosheth is still a direct descendant of Saul, and could therefore prove to be David's adversary in the case that he raises another succession struggle. David wishes to show kindness to Mephibosheth, but he also wants to maintain control over all Saul's descendants so that they cannot raise an insurrection against him.
Still, David's actions here are certainly more kind than what is typically observed in this historical period when victors usually kill their opponents and their families. Remember how Saul killed Ahimelech and all of the priests of Nob? And they weren't even resisting him. David's action here is prudent (for the sake of maintaining control), but it is also shows that David's veneration for "the LORD's anointed" extends beyond Saul and to Saul's family. Like when David objected to the murder of Ish-Bosheth, David now refuses to shed innocent blood.
There will be a bit of drama related to Mephibosheth later in this book, but he will never actually resist David in his lifetime.