The "Serpent" always had demonic connotations, starting from the devil in the garden in Genesis, ( Our Lady crushing his head) and the serpent cursed by God to a life of slithering on it's belly and eating dirt for eternity .
Please explain why , when the Israelites were bitten by a plague of snakes that Moses constructed a bronze serpent and lifted it on a pole which when gazed upon healed the people of the poisonous venom?

Jesus used this analogy  of Moses lifting up the serpent in reference to His own crucifixion:
John 3:14
"And as Moses lifted up the serpent in the desert, so must the Son of man be lifted up:"

I understand the correlation of looking upon that which was "lifted up" in order to be healed; but why the comparison with the serpent? Why the serpent at all?

I don't get that part.

Numbers 21:5-9
And speaking against God and Moses, they (the Israelites) said: Why didst thou bring us out of Egypt, to die in the wilderness?  There is no bread, nor have we any waters, our soul now loatheth this very light food. 
Wherefore the Lord sent among the people fiery serpents, which bit them and killed many of them.
Upon which they came to Moses, and said: We have sinned because we have spoken against the Lord and thee: pray that He may take away these serpents from us.  And Moses prayed for the people.
And the Lord said to him: Make a bronze serpent and set it up for a sign: whosoever being struck shall look on it shall live.  
Moses therefore made a brazen serpent, and set it up for a sign: which when they that were bitten looked upon, they were healed.

Our Lord came to save us from our sins by sacrificing Himself at the Crucifixion as a Sign of Redemption for all those who would believe in Him.  He references Moses and the serpent staff, because it prefigured this.  

I understand what you are saying, but it doesn't answer my question. Why a bronze serpent on a pole to heal the serpent's bites? What is the meaning of that?
Christ of course was lifted up on the Cross  for redemption of our sins and transgressions, just as the bronze serpent was lifted up- but the analogy was in the lifting up (and gazing upon) and not in the serpent itself.

Unless you are saying that the serpent prefigured Christ in it's image , but I don't think you do. There can be no comparisons with the serpent and our Lord.

Unless the use of the serpent has an alternate meaning here? I feel that there is something very important here to understand and i am missing it.

Him, who knew no sin, he hath made sin for us: that we might be made the justice of God in him.

- 2 Corinthians 5:21

In taking on the punishment of all sin on the Cross, Christ was "made sin". Origen writes that just as Christ had the likeness of a sinful man of the cross, yet Himself was sinless, the bronze serpent had the likeness of a living one (serpents generally representing sin or death), yet cured the Israelites of the punishment from their sins