In this chapter, David flees from Saul into the wilderness.
If there's one big message we can take from this chapter, I think it is to contrast between Saul and David's responses to the Philistines. In the first half of the chapter, David is told that the Philistines are attacking, and he responds by rescuing the town. Both David and his men are afraid of rescuing Keilah, because it is a town in Judah (only previously mentioned in Joshua 15:44 which describes the inheritance of Judah) and much closer to the center of power for Saul. Saul responds to this by trying to trap and kill David.
In the second half of the chapter, Saul is chasing David and only leaves to go defend against the Philistines. But where was Saul when Keilah was attacked? Why was David, this vagabond hiding in the desert, the person who first responded to a Philistine raid on Israel? If the previous chapter showed Saul's growing paranoia and murderous tendencies, this chapter shows us Saul's delinquency in protecting the people who are under his rule. Saul did not have any problem mobilizing his entire army to chase down David both in Keilah and following him to the wilderness of Ziph (in southern Judah, the Negev desert). This shows that Saul has full control over Israel's military, but he is using primarily to protect himself from what he perceives as threats, rather than protecting the people that he is supposed to be the leader of. Like so many other leaders throughout history, he is using his position of authority to serve himself, rather than serving the people. David is already acting more like a real king than Saul.
Secondly, we can see how heavily David depends on the LORD for guidance. First he asks twice if he should go down and save Keilah, because they were afraid of being attacked by Saul. Then he asks twice if Saul will attack and his men be given over by the townspeople (who they just saved). Each time David acted he consulted with Abiathar and the ephod to find out what the LORD would have him do, so each time he acted correctly even at great personal peril.
After that, we see Jonathan go out to encourage David. Again, it's interesting how easily David's allies find him when David is so hard to catch for his enemies. This is the last time we will see Jonathan alive; the next time he is mentioned in this book is when he is killed in battle. I talked about Jonathan a lot the last time he was mentioned in 1 Samuel 20, but the gist of it is that Jonathan was not able to escape his father's influence, and was therefore drawn into his father's destiny.
I think verse 17 tells us what is much closer to God's plan for the kingdom, that Jonathan should have been David's second-in-command while David is king. This is probably what God would want for Jonathan's life, but unfortunately it won't happen. It's very interesting also that Jonathan would tell David he's going to be king over Israel, because Jonathan was not present when David was anointed. It's possible David told him about it, but there's no mention of that in the text.
In the last part of the chapter, after being betrayed by the Ziphites (a clan of Israel), David runs away from Saul, with David and his men on one side of the mountain and Saul and his men on the other side of the mountain. This is another one of the humorous-but-serious things, which is serious because David is running for his life, but humorous because it gives me a mental image of two people running in circles around a table or something like in a cartoon. But like Laban's men chasing Jacob (Gen 31), the pursuers are always faster, so David would have certainly been caught except that at the last minute, Saul receives a message that diverts him away to defend his nation (one of the first good things he's done in the last couple chapters). This is another deliverance from the LORD, even though it looks like a coincidence.