In Genesis 3:15 God speaks to the snake in Eden:
And I will put enmity
between you and the woman,
and between your offspring and hers;
he will crush your head,
and you will strike his heel.” (3:15 ESV)
Taken literally that would be read to mean that there would be enmity between snakes and humans from then on. Humans would try to kill snakes by crushing their heads, and snakes would strike back at the heels of humans.
However use of this passage later in the Bible makes it clear that there is a deeper non-literal meaning, referring to Jesus.
The offspring of the snake is sin and the offspring of Eve is Jesus. Jesus would kill sin by overcoming sin himself (Hebrews 2:14), and allowing everyone else to overcome sin through forgiveness because of his death. On the other hand, sin struck back and Jesus was killed, although not for long.
14 Since therefore the children share in flesh and blood, he himself likewise partook of the same things, that through death he might destroy the one who has the power of death, that is, the devil, (Hebrews 2:14 ESV)
James 1 : grandmother Desire, and grandson Death
There is a similar family tree in James 1, but with three generations not two. Desire becomes pregnant with sin, sin when he is full grown fathers a son, death:
14 But each person is tempted when he is lured and enticed by his own desire. 15 Then desire when it has conceived gives birth to sin, and sin when it is fully grown brings forth death. (James 1:14-15 ESV)
If we compare Genesis 3:15 with James 1:15 it seems that the son of the serpent is sin, and it is sin that Christ triumphed over. Death (the grandson) is merely a consequence, so destroying the father also destroys the grandson.
Allusions to Genesis 3:15 later in the Bible
The first connection between the death of Christ and a serpent is between Numbers 21:19 where Moses lifted up a bronze serpent to heal the Israelites of snake bite, which Jesus compares to himself when he tells Nicodemus
And as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up, 15 that whoever believes in him may have eternal life. (John 3:14-15)
However those being bitten on the heel here are the Israelites, and Jesus being “lifted up” (on the cross) is not a direct reference to Genesis 3:15. The first clear allusion to the Genesis passage comes in Psalm 91:
12 On their hands they will bear you up,
lest you strike your foot against a stone.
13 You will tread on the lion and the adder;
the young lion and the serpent you will trample underfoot. (Psalm 91:12-13 ESV)
This pair of verses is interesting in that verse 12 is the verse that the tempter in the wilderness quotes to Christ to induce him to perform a miracle of jumping off the pinnacle of the temple. But the “devil” stops short of quoting the next verse, verse 13, which is the only verse in the Old Testament specifically connecting the Messiah to come with Genesis 3:15.
Revelation twice refers to the “dragon” as “that ancient serpent, who is called the devil and Satan” (Revelation 12:9, 20:2) and this has led to confusion among those who take the devil in the sense of a literal fallen angel, drawn on Jewish apocryphal and apocalyptic literature, as to how the serpent is the devil, and the son of the serpent is also the devil. This is is one of the reasons why many Christians view the seed of the serpent as being wicked people. The problem with this (in additional to all the other problems with belief in fallen angels) is that while Jesus did crush the head of the parent serpent – temptation desire, Jesus was still tempted, and the actual devil destroyed was not temptation itself, but giving into temptation – sin.
The disciples and the church
In the New Testament we find the “trample on serpents” figure being used of the 72 disciples (Luke 10:18-19) and the church in Rome (Romans 16:20):
18 And he said to them, “I saw Satan fall like lightning from heaven. 19 Behold, I have given you authority to tread on serpents and scorpions, and over all the power of the enemy, and nothing shall hurt you. (Luke 10:18-19)
The God of peace will soon crush Satan under your feet. The grace of our Lord Jesus Christ be with you. (Romans 16:20)
Here the son of the serpent in Genesis 3:15 is identified as Satan, understood by Jewish readers as a personification of sin.
See also What is the sin-animal crouching at Cain’s door in Genesis 4:7? : Cain is neither of the offspring referred to in Genesis 3:15. He did not fight sin at all — instead he was ruled by sin (1 John 3:12).