In this chapter, Jephthah and his Gileadite clansmen get into a war with Ephraim.
Remember when I said in Judges 9 that the loose affiliation between the tribes of Israel was falling apart? In this chapter it becomes an all-out war between Manasseh and Ephraim. Specifically it is the Transjordan Gileadite clan, the largest and most powerful clan of Manasseh, which has been the source of at least one other judge (Jair, and possibly Gideon who is a Manassite but not necessarily from Gilead).
In general, I think this story is a very strong parallel to when the men of Ephraim (again) complained to Gideon about this exact same issue, that they did not get "called up" to fight against the invaders of their time (in that case, Midianites; in this case, Ammonites).
The Ephraimites are correct in one sense; they didn't get called up to fight against the Ammonites. In another sense, Jephthah is also correct; the Ammonites have been stomping around in Israelite territory for something like 17 years and there is no indication Ephraim has done anything about it in that time. Why should Jephthah be obligated to invite the Ephraimites whenever Gilead goes to fight their national enemies? The Ephraimites are probably seeking both the honor of victory and the spoils of war, so now they respond with jealousy and anger towards the Gileadites.
I think Jephthah is largely correct in what he says, but at the same time, his words resulted in a battle between Gilead and Ephraim. Gilead was victorious, but Israel (as a whole) was defeated. There is no victory in destroying a brother tribe, and while Jephthah was victorious over Ammon, this is yet another grim conclusion to what was otherwise a victory for the people of Israel.
In addition, this story is commonly contrasted with the very similar event in Judges 8 when the men of Ephraim contended against Gideon for the same reason. The big difference is that Gideon was able to assuage their hurt feelings by emphasizing their glory in killing the two kings of Midian. In this story, Jephthah responds with anger, which is perhaps justified, but nevertheless results in a war between two tribes. This is another example of how things are progressively getting worse in Israel as time passes. Many commentators view Gideon favorably compared to Jephthah for this reason, although Gideon had some issues of his own (which I also discussed in Judges 8).
There are a few judges after Jephthah in this chapter, but all of them are relatively inconsequential (and never mentioned again).
The last thing I will mention about this chapter is the funny little story about "shibboleth". As obscure as this story may seem, it is the origin of an English phrase, "shibboleth", which means basically like a password or code phrase of some kind. Sometimes, as here, it refers to particular regional pronunciations of a word that reveal the hometown of the speaker. I think I have also heard it used in reference to authentication techniques in computer security. So this is just another way that biblical stories have influenced modern English idiom.