These notes by Matthew Henry add some light to Jephthah's vow to offer whatever comes out of the door of his home as a burnt offering.
Several important lessons are to be learned from Jephthah's vow.
1. There may be remainders of distrust and doubting, even in the hearts of true and great believers.
2. Our vows to God should not be as a purchase of the favour we desire, but to express gratitude to him.
3. We need to be very well-advised in making vows, lest we entangle ourselves.
4. What we have solemnly vowed to God, we must perform, if it be possible and lawful, though it be difficult and grievous to us.
5. It well becomes children, obediently and cheerfully to submit to their parents in the Lord. It is hard to say what Jephthah did in performance of his vow; but it is thought that he did not offer his daughter as a burnt-offering. Such a sacrifice would have been an abomination to the Lord; it is supposed she was obliged to remain unmarried, and apart from her family. Concerning this and some other such passages in the sacred history, about which learned men are divided and in doubt, we need not perplex ourselves; what is necessary to our salvation, thanks be to God, is plain enough. If the reader recollects the promise of Christ concerning the teaching of the Holy Spirit, and places himself under this heavenly Teacher, the Holy Ghost will guide to all truth in every passage, so far as it is needful to be understood.
I believe God included the story of Jephthah's vow to emphasize the seriousness of making a vow to the Lord, not to show that this was an acceptable practice that God approved of. Every where else in Scripture where burnt offering is mentioned, except for Gen 22, burnt offering deals with the death of an animal. Even in Gen 22, God provided the ram for the burnt offering in the place of Abraham's son.