According to speaker Ray Vander Laan (RVL), who has spent time in the rural areas of the Middle East, this ceremony is still conducted today. The significance is that each of the two parties involved in the covenant would then walk through the blood draining from the animals, symbolically stating that if he failed to keep his end of the bargain, the other party has permission to stomp the covenant-breaker's blood into the ground.
RVL continues, saying that the smoking fire pot and the flaming torch are both symbols for the God of the Bible.
God had promised to Abram to make of him a great nation, to give him all the land in the area, and to bless the nations through his seed (this last item being cited by Paul in Gal 3:8 as being "the gospel"). For his part, Abraham's role was simply to live in God's presence and "be perfect" (Gen 17:1), which of course, obviously, was sure to result in a broken covenant on Abraham's part.
So when it was time to perform the covenant ceremony, God passed through the split animals as a smoking fire pot; then when it was Abram's turn to pass through, God took Abram's turn, passing again as a flaming torch.
In essence, God was saying, "If I fail to keep my end of the bargain, you may stomp my blood into the ground. And if you fail to keep your end of the bargain, you may stomp my blood into the ground." At that moment, God sealed the fate of his son Jesus to be killed at the hands of men.
We see the same type of covenant ceremony in Jeremiah 34. When YHWH gave the Law of Moses on Mount Sinai centuries earlier, one of the provisions was that if any member of the community sold himself into slavery (a common practice for those in poverty), he was to be freed in the seventh year (Ex 21:1; Deut 15:12; Jer 34:14). But the Israelites had not been keeping that practice, and YHWH condemned them for not keeping it, saying:
HCSB Jer 34:18 As for those who disobeyed My covenant, not keeping the terms of the covenant they made before Me, I will treat them like the calf they cut in two in order to pass between its pieces. 19 The officials of Judah and Jerusalem, the court officials, the priests, and all the people of the land who passed between the pieces of the calf 20 will be handed over to their enemies....