This ceremony raises several questions. Is there any significance to the type of animals chosen? One answer (see Genesis Rabbah 44:14,15, Rashi on 15:6,9 and Rambam on 15:10), is that prior to the ceremony Avram has asked by what merit would his descendants would inherit the land and G-d answered him by the merit of the sacrifices. Thus, the choice of animals was because G-d was instructing Avraham which animals would be suitable for sacrifices. Benno Jacob (1974, p.101, quoted by N. Leibowitz, 1976, p. 149) argues that the ceremony here has no connection with sacrifices since there was no altar, no blood was poured out and nothing was burnt. Instead, he suggests that the animals were simply chosen because they were available. Another possibility is that though the animals were not meant as sacrifices still they had to be pure animals since the fire that passed through them symbolized G-d's presence.
Why were the mammals divided? Rashi (on 15:10) explains that the ancient way to make a covenant was for an animal to be split and for the partners in the covenant to pass through the divided animal. Thus, in Hebrew the description for making a covenant is literally called to cut a covenant. Rashi quotes Jeremiah 34:18-20 which records that the princes of Yehuda and Yerushalayim passed between a divided calf in order to impress upon them that if they did not keep the covenant, then they would be punished and would become food for the animals. The passing through the animals was a type of self-imprecation, where the person accepts upon himself a potential punishment for not upholding his part of the covenant.
The idea would then be that the mammals were divided in order for the fire to pass through them, and this passing through established the covenant. Yet, can the passing of the fire through the animals signify the idea of self-imprecation as occurs in Jeremiah 34? Was G-d calling upon Himself a future punishment? Gerhard Hasel (1981) argues that one cannot compare Jeremiah 34 to Bereshit 15 since it cannot be that G-d is making a self-imprecation. Instead, he points out that ancient treaties from the second millennium BCE invoke the killing of an animal as a "rite of treaty ratification, symbolizing the binding status of the covenanting parties," and by these treaties there was no evidence that one or both parties to the treaty passed through the animals. Thus, just the cutting of the animals signified the making of the covenant. Why then did the fire pass through the pieces? Hasel suggests that this act was a divine ratification of the covenant that G-d "irrevocably pledged the fulfillment of His covenant promise to the patriarchs." Another possibility is from the Rashbam (on Shemot 24:11 and Shemot 33:18) that the fire was an example of a theophany which accompanies all the covenants with G-d.
Why did Avram not pass through the animals either before or after the fire? Maybe Avram did not need to pass between the animals since the covenant did not obligate him in anyway because the covenant was G-d's promise that Avram's descendants would inherit the land. In addition, as explained by Hasel, there was no need for Avram to pass through the animals since the covenant was made just by the cutting up of the animals.
Why were the birds not divided? Ramban (on 15:10, also see Hizkuni) explains that since there were two birds one could be placed facing the other, and then there was no need to cut up the birds. Thus, in total there were two columns (or rows) with each column having half a calf, half a goat, half a ram and a bird.
Why was there a need for three mammals and two birds? In the ceremony recorded in Jeremiah only one calf was divided. Why here was one animal not sufficient? Many commentators have viewed the number of animals as having a symbolic message. For example, Rashi (on 15:10, also see Radak) suggests that the mammals were symbolic of the nations of the world, while the Jewish people were symbolized by the birds.
Benno Jacob (1974, p. 103, also see S. R. Hirsch 1989, pp. 278, 279, on 15:9) writes that the animals are related to the ensuing prophecy of 15:13-16. The three divided animals represented the three generations that would suffer slavery in Egypt, while the birds, which were not divided, symbolized the generation that would go free. This makes a connection between Avram's action with the animals and the prophecy of the slavery in Egypt. Yet, it is not clear how the division of the animals relates to the suffering in Egypt and we have no knowledge how many generations actually were slaves in Egypt. Furthermore, the end and the crucial point of the prophecy is that the fourth generation would return to the land of Israel, but according to this symbolism the birds just symbolize that the fourth generation goes free from Egypt and do not indicate that the generation would return to the land of Israel. However, the idea of relating the symbolism of the animals to the ensuing prophecy and to the numbers three and four is logical because in total there were four animals in each column and the number three is stressed both by the age of the mammals and by the fact that there were three mammals.
In the ensuing prophecy, 15:16 records that the fourth generation would return to the land of Israel, and I believe that this prophecy is referring to Yosef. (See our discussion on Bereshit 15:16, "Who is the fourth generation in the prophecy of the covenant of the pieces?") Therefore, my guess is that the four sets of animals relate to the history of the generations of Avram and his immediate descendants. In each of the first three generations, there was a split in the family, Avram and Lot, Yitzhak and Yishmael, and Yaakov and Esav. These separations in Avram's family were symbolized by the division of the mammals. The fourth generation began as two families, the sons of Lea and Rahel, which is symbolized by the two birds, but in the end this generation joined together when Yehuda risked his life for Binyamin (45:18-34), and this is symbolized by the fact that the birds were not divided.
The unity of the fourth generation explains an anomaly of the text. 15:9 refers to two birds, but 15:10 uses the singular term bird. It is true that the singular can function as a collective noun, but why not use the plural? Radak writes that the use of the singular symbolizes that all the Jewish people would be unified even when they were dispersed throughout the world, but I think it signifies the unity of the fourth generation, the children of Yaakov.
I believe that the prophecy of the return of the fourth generation refers to Yosef and his generation (see discussion below on 15:16, "Who is the fourth generation?"). With this understanding, there is a parallelism between the symbolism of the number of animals and the ensuing prophecy, that both refer to the set of same four generations that begins with Avram.
15:11 records that vultures attempted to eat the animals, and Avram chased them away. It seems that the vultures attempted to eat all of the animals, but Radak argues that the vultures only attacked the birds. In any event, why is this action by the vultures and Avram recorded in the Torah? Again, these actions are viewed as being symbolic; see for example comments of the Ramban and Radak (on 15:11).
My guess is that the symbolism is that the covenant is unconditional. If the vultures just attempted to eat the birds, who according to my understanding refer to the fourth generation, then the message is that the promise that the fourth generation would return to the land of Israel was unconditional. On the other hand, if the vultures attempted to eat all the animals, then the idea is that the promise of land to all of the four generations from Avraham was unconditional. Thus, the Jewish people were forbidden from taking the land of Lot's children, Moav and Ammon, and Esav's children when they marched towards the land of Israel, Devarim 2:5,9,19. With regard to the Yishmael 17:20 and 21:13 record G-d's promise that his children would become a separate nation and 25:18 records that they lived in a wide expanse of land.
Hasel, Gerhard, 1981, The meaning of the animal rite in Genesis 15, Journal for the Study of the Old Testament, 19, pp.61-78.
Hirsch, S. R. (1808-1888), 1989, The Pentateuch, rendered into English by Isaac Levy, second edition, Gateshead: Judaica Press.
Jacob, Benno (1869-1945), 1974, The first book of the bible: Genesis, commentary abridged, edited and translated by Earnest I. Jacob and Walter Jacob, New York: Ktav Publishing House.
Leibowitz, Nehama (1905-1997), 1976, Studies in Bereshit, translated by Aryeh Newman, Jerusalem: The World Zionist Organization.