The episode can we watched here. (Dialogue expanded and edited somewhat)
The Fourth Gospel has two main messages, throughout - one is to make clear the nature of Jesus, his divinity, that he is the Son of God sent by his Father; the other message is to teach about the life everlasting Jesus will give to those who follow him, who believe him - who love and have faith in him.
The mysterious aspects of the Jacob's well episode are concerned with Jesus teaching, using symbols, about the possibility and nature of life everlasting. The main symbol is water - as befits the setting at a well. And indeed Jesus is teaching by using the symbol the woman suggests - starting from the literal water to mean something much more.
When we consider symbolism as used 2000 years ago we need to be open to the fact that words then had large, more multiple-simultaneous meanings than they do now (by contrast modern words tend towards single, narrower and more precise meanings). This is rooted in a different, more 'poetic' way of thinking in ancient times. It is the 'poetic' that enables us to understand across the gulf of consciousness.
We need to allow ourselves to understand this text in the way we understand poetry - and this is possible because the 'King James' version of the Bible is divinely-inspired and consequently probably the single most 'poetic' work of prose in the language. But because this is like poetry; as I would when 'explaining' a poem, I will try to made some helpful suggestions but without dissecting.
As well as the two main themes, there is a subordinate theme related to fact that although Jesus is the Jewish Messiah, his gift of life everlasting is for all Men - including those such as Samaritans who have a bad relationship with the 'mainstream' Jews. This is, indeed, how the dialogue opens, with Jesus breaking what was apparently a taboo relating to interactions with Samaritans.
These three themes weave through the dialogue: that Jesus is the Messiah, that he brings, now ('the hour cometh') a new possibility of life everlasting, and that this gift is for all (including Samaritans). Because Jesus is the Messiah, he can give her more than 'merely' the good water of this well he asks of her; if she asks, Jesus could give her 'living' water (life everlasting, eternal life). And while after even the best ordinary water, a mortal Man will 'thirst again' (will be subject to corruption and death); after the water (life) that Jesus gives, a Man would never thirst again (he would live forever).
The woman then challenges Jesus's ability to make this promise - saying that even the great Patriarch Jacob could offer only good ordinary water. Then Jesus reveals he is the Messiah, and that 'the hour cometh, and now is' when Jews and Samaritans will both have a new religion, both unite in this promise of 'living water'.
The fact that the Jesus told the woman all things that she ever did, is indicated by the snippet concerning her marital and cohabiting history. But presumably there were, in addition, other more striking items that made the women regard Jesus's knowledge as miraculous; and convinced many others in her city.
Why the mention of husbands, then? I'm not sure - one aspect may be that the woman was apparently loose in her sexual morals; although this seems contradicted by the fact that so many men in her city believed her account of meeting meeting the Christ to the point of travelling to see for themselves. In general, I feel something is missing from the Gospel here - in particular there is a discontinuity with 4:20 when the conversation jumps from the husbands to 'Our fathers worshipped in the mountains' and a new line of discussion.
When the disciples find Jesus at the well, apparently just as the Samaritan woman leaves; Jesus embarks on a new symbolism about 'meat' - again correcting the mundane reference to eating used by the disciples. In essence, meat - the most concentrated food - seems also to be something like a Man's personal destiny, his role, his task - Jesus's task. And perhaps that many Men have the task of completing work begun by another - as the disciples need to continue the work of Jesus.*
In general, through the Fourth Gospel, the method is often used by Jesus of taking a mundane, narrow meaning of a word, and expanding it symbolically; and he does this to indicate the qualitative nature difference between this mortal life and the resurrected life eternal. Thus: the difference between well water and living water; the difference between meat as nourishment and the meat of Jesus's ministry.
*Also John 6:27 - Labour not for the meat which perisheth, but for that meat which endureth unto everlasting life, which the Son of man shall give unto you: for him hath God the Father sealed. 54-6 Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day. For my flesh is meat indeed, and my blood is drink indeed. He that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him.
Here it may be that meat symbolises the conduct of life (work/ task). Blood when drunk may be akin to water, but with also a meaning of love (to drink Jesus's blood being to believe, have faith, love him). Thus we get something like: he that conducts his life ('labours') according to its everlasting destiny (the meat which endureth), and 'labours' not for worldly-goals which perisheth; and is then resurrected to eternal life; becomes a fully divine brother to Jesus (mutual dwelling-in; i.e. a loving relationship with direct knowledge of each other).
John 4: 5 Then cometh he to a city of Samaria, which is called Sychar, near to the parcel of ground that Jacob gave to his son Joseph. 6 Now Jacob's well was there. Jesus therefore, being wearied with his journey, sat thus on the well: and it was about the sixth hour. 7 There cometh a woman of Samaria to draw water: Jesus saith unto her, Give me to drink. 8 (For his disciples were gone away unto the city to buy meat.) 9 Then saith the woman of Samaria unto him, How is it that thou, being a Jew, askest drink of me, which am a woman of Samaria? for the Jews have no dealings with the Samaritans. 10 Jesus answered and said unto her, If thou knewest the gift of God, and who it is that saith to thee, Give me to drink; thou wouldest have asked of him, and he would have given thee living water. 11 The woman saith unto him, Sir, thou hast nothing to draw with, and the well is deep: from whence then hast thou that living water? 12 Art thou greater than our father Jacob, which gave us the well, and drank thereof himself, and his children, and his cattle? 13 Jesus answered and said unto her, Whosoever drinketh of this water shall thirst again: 14 But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life. 15 The woman saith unto him, Sir, give me this water, that I thirst not, neither come hither to draw. 16 Jesus saith unto her, Go, call thy husband, and come hither. 17 The woman answered and said, I have no husband. Jesus said unto her, Thou hast well said, I have no husband: 18 For thou hast had five husbands; and he whom thou now hast is not thy husband: in that saidst thou truly. 19 The woman saith unto him, Sir, I perceive that thou art a prophet. 20 Our fathers worshipped in this mountain; and ye say, that in Jerusalem is the place where men ought to worship. 21 Jesus saith unto her, Woman, believe me, the hour cometh, when ye shall neither in this mountain, nor yet at Jerusalem, worship the Father. 22 Ye worship ye know not what: we know what we worship: for salvation is of the Jews. 23 But the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth: for the Father seeketh such to worship him. 24 God is a Spirit: and they that worship him must worship him in spirit and in truth. 25 The woman saith unto him, I know that Messias cometh, which is called Christ: when he is come, he will tell us all things. 26 Jesus saith unto her, I that speak unto thee am he. 27 And upon this came his disciples, and marvelled that he talked with the woman: yet no man said, What seekest thou? or, Why talkest thou with her? 28 The woman then left her waterpot, and went her way into the city, and saith to the men, 29 Come, see a man, which told me all things that ever I did: is not this the Christ? 30 Then they went out of the city, and came unto him. 31 In the mean while his disciples prayed him, saying, Master, eat. 32 But he said unto them, I have meat to eat that ye know not of. 33 Therefore said the disciples one to another, Hath any man brought him ought to eat? 34 Jesus saith unto them, My meat is to do the will of him that sent me, and to finish his work. 35 Say not ye, There are yet four months, and then cometh harvest? behold, I say unto you, Lift up your eyes, and look on the fields; for they are white already to harvest. 36 And he that reapeth receiveth wages, and gathereth fruit unto life eternal: that both he that soweth and he that reapeth may rejoice together. 37 And herein is that saying true, One soweth, and another reapeth. 38 I sent you to reap that whereon ye bestowed no labour: other men laboured, and ye are entered into their labours. 39 And many of the Samaritans of that city believed on him for the saying of the woman, which testified, He told me all that ever I did. 40 So when the Samaritans were come unto him, they besought him that he would tarry with them: and he abode there two days. 41 And many more believed because of his own word; 42 And said unto the woman, Now we believe, not because of thy saying: for we have heard him ourselves, and know that this is indeed the Christ, the Saviour of the world.