Genesis 15:17 reads “And it came to pass, that, when the sun went down, and it was dark, behold a smoking furnace, and a burning lamp that passed between those pieces.”, where pieces refers to the elements of the sacrifice that Abram had brought before God.

So while it was dark, we see a smoking furnace and a burning lamp passing between the sacrifice. What could this mean?
Some commentaries exposit and state that the smoking furnace refers to the afflictions of the Israelites (the seed of Abram) would face and they get their basis from other scriptural texts which portray
– the Egyptians who enslaved the Israelites as a furnace of iron (1 Kings 8:51),
– the Assyrian (Sennacherib), who besieged the Israelites whose reign was symbolic of a furnace in Jerusalem (Isaiah 31:9)
They also exposit and state the the burning lamp symbolizes the salvation of the Israelites (the seed of Abram), which they exposit from the Scripture recorded in 1 Kings 11:36 and 15:4 and Isaiah 62:1. 1 Kings 11:26 and 15:4 both express the words of God, who for David’s sake, said that there will be a lamp who will be set forth establish Jerusalem. Isaiah 62:1 refers this lamp that burns as one of salvation.

While these are certainly plausible, I am convinced that the two symbols here, of the smoking furnace, and the burning lamp are symbolic of the persons of the Triune Godhead and I deduce these, not by mere opinion, but by substantiating text in the Bible.
First, the smoking furnace and burning lamp were animate and passed through the pieces of the sacrifice, accepting the sacrifice that was offered and so it is less likely that these symbols directly meant the afflictions and salvation of Israel, as the commentators state. Furthermore, Exodus 19:18 states that when the LORD God descended upon mount Sinai in fire, the mount was altogether in smoke, which ascended as the smoke of a furnace. So this makes me believe that the smoking furnace is symbolic of God, the Father, the first person of the Trinity.
I must admit that the identity of the burning lamp is a little more ambiguous. On one hand, it could be symbolic of Jesus Christ, the second person of the Trinity, who is the light of the world, who shined out in the darkness as a burning lamp. When Jesus walked with the men on the road to Emmaus, they felt their hearts burn within them (Luke 24:32), which further accentuates this proposition that Jesus is the burning lamp. On the other hand, it is also possible that the burning lamp could be symbolic of the Holy Spirit of God, the third person of the Trinity, who though being one (Ephesians 4:4) is expressed as seven lamps of fire before the throne of God (Revelation 4:5), in whose midst stands Jesus Christ, the lamb of God (Revelation 5:6). Herein, we get a glimpse of the Triune God in One (God the Father, Jesus Christ the Son and the Holy Spirit God) all at work in the acceptance of the sacrifice offered by Abram.

Points to ponder:
If you/I were to offer your life as a living sacrifice today, would you/I have the Triune God in one passing through your/my life and accepting the sacrifice of our life, while we live in a dark sinful world? Would you/I see a smoking furnace and a burning lamp pass through your/my life? Think about it.

Genesis 15:17 (KJV)
17 And it came to pass, that, when the sun went down, and it was dark, behold a smoking furnace, and a burning lamp that passed between those pieces.

Exodus 19:17-19 (KJV)
17 And Moses brought forth the people out of the camp to meet with God; and they stood at the nether part of the mount.
18 And mount Sinai was altogether on a smoke, because the Lord descended upon it in fire: and the smoke thereof ascended as the smoke of a furnace, and the whole mount quaked greatly.
19 And when the voice of the trumpet sounded long, and waxed louder and louder, Moses spake, and God answered him by a voice.

Luke 24:32 (KJV)
32 And they said one to another, Did not our heart burn within us, while he talked with us by the way, and while he opened to us the scriptures?

Isaiah 62:1 (KJV)

1 For Zion’s sake will I not hold my peace, and for Jerusalem’s sake I will not rest, until the righteousness thereof go forth as brightness, and the salvation thereof as a lamp that burneth.