The story of Yiftach's vow is told in the eleventh chapter of Sefer Shoftim and is read as the haftara for Parashat Chukat. Before leaving to wage battle against the nation of Amon, Yiftach vows to God that should he return victorious, he will designate as an offering "the first that leaves the doors of my home to greet me" (Shoftim 11:31). Tragically, it is Yiftach's daughter who first greets him upon his triumphant return home from battle. (the commentators debate as to whether Yiftach actually brought his daughter as an offering, or subjected her to a life of celibacy.)
It is commonly understood that Yiftach made this vow under the assumption that an animal normally brought as a sacrifice – such as a sheep or goat – would be the first to greet him. This reading, however, leaves us wondering why he would make such an assumption. Furthermore, Yiftach specifies that he designates as an offering the first that "leaves the doors of my home," indicating that he refers to that which is normally in the home and comes out to greet him upon his return. It is hard to imagine that his family's sheep and cattle were kept inside the house; seemingly, he refers to human beings, presumably his family members.
Rav Yigal Ariel, in his Oz Va-anava (pp. 212-3), thus explains that Yiftach in fact had his family in mind when uttering this vow. In an attempt to exude piety and selfless devotion to God and to Am Yisrael, Yiftach proclaimed as he left for battle that he is prepared to sacrifice as an offering the first family member that greets him upon his return. This proclamation, however, according to Rav Ariel's understanding, was made disingenuously. Yiftach never had any intention of sacrificing a family member; he assumed that everybody would learn of his vow and thus ensure not to leave the home to greet him as he returned from battle. The vow was uttered purely as a tactical exhibition of piety, and not as a sincere but misplaced act of devotion. Tragically, Yiftach's daughter was unaware of her father's proclamation, and Yiftach felt unable or unwilling to seek the annulment of his vow.
Rav Moshe Hattin (http://vbm-torah.org/archive/shoftim65/09shoftim.htm) likewise suggested that Yiftach refers to a human being, rather than an animal, but develops a much different theory. The introductory verse to this section (Shoftim 11:6) tells of Benei Yisrael's abandonment of their spiritual heritage and embrace of numerous foreign modes of worship. And although they responded to the Amonite persecution by discarding their foreign deities (11:16), it is nevertheless likely that many values and mores of the surrounding nations were still part of their mindset and routine. Rav Hattin suggests that Yiftach actually intended all along to offer a human sacrifice – a ritual that was indeed common among the ancient pagans. He did not, however, intend that his "sacrifice" would be his daughter. He had assumed that a clan member, distant relative, servant or casual visitor would be the first to greet him upon his return from battle, and did not figure that it might be his daughter. Yiftach reacted with horror upon seeing his daughter because he had intended on designating as the human sacrifice some other individual, and not his own family member.
In any event, according to this theory, the story of Yiftach's vow demonstrates the extent to which pagan culture had become entrenched among Benei Yisrael – that even after their rejection of paganism, their leader still deemed it an act of piety and devotion to offer a human sacrifice.
Courtesy of Yeshivat Har Etzion - www.etzion.org.il