Serpents represent what we know from our bodily senses, and the reasoning based on our senses. Since the people of the Most Ancient Church had become more external, they were susceptible to the lure of trusting their senses more than they trusted the leading of the Lord. That was particularly true for the sense of self the people had been given, which is represented by the woman. Eating of the trees in the garden represented taking in desires for good and true ideas from the knowledge granted them by the Lord.

So here, for the first time, we see people, from their own senses, actually questioning the Lord. From their senses they wished to explore the knowledge represented by fruit of the garden, but wondered why they were denied the tree of knowledge.

(References: Arcana Coelestia 194, 195, 196, 197)

197. With the most ancient people, who were celestial, a serpent meant being completely watchful, and so also meant their sensory perception by means of which they were to show vigilance to avoid being harmed by the evil. This is clear from the Lord's words to His disciples,

Behold, I send you out as sheep in the midst of wolves; so be shrewd as serpents and simple as doves. Matthew 10:16.

And also 'the bronze serpent' which was raised up in the wilderness and which meant the Lord's Sensory Perception. He alone is Celestial Man, and He alone is completely watchful and provides for everybody. Whoever beheld it therefore was delivered.