Jonathan really, really loves David. In a totally brotherly way, of course!
David flees the court, either with Jonathan or to wherever Jonathan is, it isn't clear. He asks him how he sinned. Rather than answer, Jonathan promises to spy for him. They make another covenant.
David decides to hide the next day, and Jonathan is to say that he went home for an emergency sacrifice. They'll know by Saul's reaction whether he's currently possessed by god's evil spirit. Jonathan prays to god that if he doesn't protect David, the lord's wrath shall befall his household.
So, David's hiding, and Saul thinks he's just off doing laundry or sacrificing because he isn't clean. The next day, he asks Jonathan where he is, and Jonathan says his piece about the emergency sacrifice in Bethlehem. Saul gets angry at Jonathan, possibly because of his homosexual affair, and orders him to go and get David so he can kill him. Jonathan asks why, and gets a javelin thrown in his direction in response.
Jonathan goes out to the field the next day with his arrow retriever, because princes are just like that, and according to the secret code worked out the day before, lets David know that his father is currently under god's demonic control. Why even bring the kid? Why not just go out and tell him?
Anyway, David comes out and they kiss and cry, and David leaves to become a rebel leader while Jonathan goes home.