The story takes place in the wilderness, just as we are in this world.  

Each of the people that were healed certainly had a testimony to remember, share and to compare.  

We are all spiritually bitten, sick, poisoned by this wilderness we are in ;snakes are everywhere and we each need healing and recovery that only God can provide.  

When we are saved by Jesus and forgiven of our sins we come away with a testimony and a few more miles to put in...but when we keep our eyes on Him we are not overtaken by our sins ; we complain less and we bite each other less too.   

We have the ability to share, compare and thank God in a way we didn't before we realized we were bitten and dying.  

The fiery serpent being raised on a pole in the wilderness was pointed to by Jesus as a shadow proto-type of Him as savior to come.

Healing came with one condition: The Israelites had to exercise faith in the offer.

[Jhn 3:14 KJV]

"And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up:"

[Jhn 3:15 KJV]

"That whosoever believeth in him should not perish, but have eternal life."

The bronze serpent was a visual representation of the wrath of God against a grumbling and complaining people.  

It was meant to remind them of  the Garden of Eden where Satan came in the form of a serpent to tempt people with sin ( which they were comitting ) and orignally caused them to be cursed with suffering and death. 

Christ crucified is a visual representation of the wrath of God against all ungodliness and unrighteousness of men who have been tempted with sin in that they die cursed at that tree.

God used the fiery serpent to humble the people...

The fiery serpent was a serpent without poison ( perhaps representing sin ), harmless and not to be worshiped, and not an idol. ( originally - although later in the bible people do sin when they make it ( the object ) an idol. 

 The people on their own without Moses would have been afraid to make an image like this perhaps out of fear of breaking God's laws.  It became a simple method of God revealing His glory to heal the people through their faith in doing what He asked of them to do....

LATER IN BIBLE : 

[2Ki 18:1 KJV]

"Now it came to pass in the third year of Hoshea son of Elah king of Israel, [that] Hezekiah the son of Ahaz king of Judah began to reign."

[2Ki 18:3 KJV]

"And he did [that which was] right in the sight of the LORD, according to all that David his father did."

[2Ki 18:4 KJV]

"He removed the high places, and brake the images, and cut down the groves, and brake in pieces the brasen serpent that Moses had made: for unto those days the children of Israel did burn incense to it: and he called it Nehushtan."

Now the word Nehushtan means a thing of brass. It's no God; it's a thing of brass.

Christ was a man without poison / sin, in the likeness of sinful flesh, but without sin.  He was made to become sin for us...He is not an idol, because He is God's method of dealing with sin in the world.  He tests people's faith in doing what He asks them to do...put their faith in Him.

 [2Co 5:21 KJV]

"For he hath made him [to be] sin for us, who knew no sin; that we might be made the righteousness of God in him."

[Rom 8:3 KJV]

"For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:"

In the world, people are dying from the deadly poison of sin; surrounded on all sides and bitten, complaining, etc.  

Often they refuse to look at Jesus.  Similar here : When they put their faith in God and what he and Moses provided for them they were healed.  

He alone is the only antidote for sin’s poison and death.

Not to be confused with Satan, Christ volunteered to die on the cross for everyone's sins, and looking to Him will heal people and they will be saved ; although some look to Him and think He is an idol instead of the Messiah, Saviour of the world, Son of God, & God in the flesh.  

[Isa 53:3 KJV]

"He is despised and rejected of men; a man of sorrows, and acquainted with grief: and we hid as it were [our] faces from him; he was despised, and we esteemed him not."

Moses prayed intercessing for the people: 

[Num 21:7 KJV]

"Therefore the people came to Moses, and said, We have sinned, for we have spoken against the LORD, and against thee; pray unto the LORD, that he take away the serpents from us. And Moses prayed for the people."

Jesus prayed intercessing for the people: 

[Luk 23:34 KJV]

"Then said Jesus, Father, forgive them; for they know not what they do. And they parted his raiment, and cast lots."

God's provision likely sounds completely crazy to the skeptic.  

The lesson here is that God tests our faith in Him and His provision, not in our own remedy for sin.  

Since this sounds foolish to look at the serpent, people choose to suffer.  Sometimes life has to get really bad before we may even consider Jesus at a more desperate moment.

[1Co 1:27 KJV]

"But God hath chosen the foolish things of the world to confound the wise; and God hath chosen the weak things of the world to confound the things which are mighty;"

Jesus said : 

[Mat 13:15 KJV]

"For this people's heart is waxed gross, and [their] ears are dull of hearing, and their eyes they have closed; lest at any time they should see with [their] eyes, and hear with [their] ears, and should understand with [their] heart, and should be converted, and I should heal them."

[Num 21:6 KJV]

"And the LORD sent fiery serpents among the people, and they bit the people; and much people of Israel died."

It seems that our trials as people of God are not unusual...we are not to complain but to look to Jesus who took on the most suffering  as a result of sin for us....

God, in His mercy, used the very thing that killed so many of them to bring them back to Him in contrition and repentance.

[1Pe 4:12 KJV]

"Beloved, think it not strange concerning the fiery trial which is to try you, as though some strange thing happened unto you:"

[1Pe 4:13 KJV]

"But rejoice, inasmuch as ye are partakers of Christ's sufferings; that, when his glory shall be revealed, ye may be glad also with exceeding joy."

The result of the fiery bites of the serpent : swelling, poison, etc. would be death.  

They were used by god as judgement...much like satan is God's instrument in bringing many to Jesus.  

[Rom 6:23 KJV]

"For the wages of sin [is] death; but the gift of God [is] eternal life through Jesus Christ our Lord."

The people didn't have to 'do' anything but have faith in what they were told.  God provided a free way : 

[Rom 6:23 KJV]

"For the wages of sin [is] death; but the gift of God [is] eternal life through Jesus Christ our Lord."

[Eph 6:16 KJV]

"Above all, taking the shield of faith, wherewith ye shall be able to quench all the fiery darts of the wicked."

Whosoever could be saved : 

[Num 21:8 KJV]

"And the LORD said unto Moses, Make thee a fiery serpent, and set it upon a pole: and it shall come to pass, that every one that is bitten, when he looketh upon it, shall live."

Whosoever can be saved still : 

[Jhn 3:16 KJV]

"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life."

Snakes shed their skin and are sort of 'reborn' or born again with a new coat on them....

During this incident the people complained they had not bread or water / only light bread : 

[Num 21:5 KJV]

"And the people spake against God, and against Moses, Wherefore have ye brought us up out of Egypt to die in the wilderness? for [there is] no bread, neither [is there any] water; and our soul loatheth this light bread."

Jesus told us we must be born again in the Spirit by believing in Him for our Salvation alone...

[2Co 5:17 KJV]

"Therefore if any man [be] in Christ, [he is] a new creature: old things are passed away; behold, all things are become new."

[Jhn 6:63 KJV]

"It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, [they] are spirit, and [they] are life."

[Jhn 3:7 KJV]

"Marvel not that I said unto thee, Ye must be born again."

[Gal 4:29 KJV]

"But as then he that was born after the flesh persecuted him [that was born] after the Spirit, even so [it is] now."

[Jhn 6:35 KJV]

"And Jesus said unto them, I am the bread of life: he that cometh to me shall never hunger; and he that believeth on me shall never thirst."