In this chapter, Saul dies in battle with the Philistines.
What Samuel prophesied beginning in 1 Samuel 13 has finally come to pass, that Saul would not remain as king over Israel, nor will his kingdom (i.e. ruling descendants) endure. Both Saul and Jonathan die. However, not all of Saul's sons are killed, so while his descendants never regain the throne, his family line is not entirely wiped out. This is actually going to result in further strife as we move into 2 Samuel.
For now, though, the Philistines carry off Saul's body and armor and weapons as trophies of their victory. In verse 11, we are told that men from Jabesh Gilead snuck into Philistine territory and buried Saul's body. Remember how Saul's first act as the anointed king was to rescue this same Jabesh Gilead from the Ammonites? The men of Jabesh Gilead remembered and they appear to have remained loyal to Saul this whole time. Even though they couldn't save Saul's life, they were able to keep him from further disgrace at the hands of the Philistines. In ancient times it was considered a great shame to have one's body kept unburied. Therefore the Philistines are keeping Saul's body upon their city wall both as a monument to their victory, but also to humiliate Saul.
This is the end of 1st Samuel, but it should be evident that it's not the end of the story, because David is still living in exile and does not yet rule over Israel. Textual evidence suggests that Samuel used to be a single book, and at some point (in antiquity, but after the book was written) it was broken into two parts, the 1st and 2nd halves of Samuel. Therefore the story of 2nd Samuel will pick up right where we leave off here.
Saul is dead, but the story of Israel is not over.