A Deeper Look Into John 2.1-11

On the third day a wedding took place at Cana in Galilee. Jesus’ mother was there, ² and Jesus and his disciples had also been invited to the wedding. ³ When the wine was gone, Jesus’ mother said to him, “They have no more wine.”
⁴ “Woman,^[a] why do you involve me?” Jesus replied. “My hour has not yet come.”
⁵ His mother said to the servants, “Do whatever he tells you.”
⁶ Nearby stood six stone water jars, the kind used by the Jews for ceremonial washing, each holding from twenty to thirty gallons.^[b]
7 Jesus said to the servants, “Fill the jars with water”; so they filled them to the brim.
⁸ Then he told them, “Now draw some out and take it to the master of the banquet.”
They did so, ⁹ and the master of the banquet tasted the water that had been turned into wine. He did not realize where it had come from, though the servants who had drawn the water knew. Then he called the bridegroom aside ¹⁰ and said, “Everyone brings out the choice wine first and then the cheaper wine after the guests have had too much to drink; but you have saved the best till now.”
¹¹ What Jesus did here in Cana of Galilee was the first of the signs through which he revealed his glory; and his disciples believed in him. John 2 NIV

Just a bit on Jewish wedding culture, since I have yet to put out my bridal posts. Jewish weddings are celebrated for seven days--a huge party with as many people as possible crowded together celebrating the bride and groom. Imagine doing such a thing today.
As another interesting thing, I can tell you that this bride was most certainly a virgin. The wedding day was on a Wednesday, the day in which virgins got married. Previously married women might get married on Thursday. The reason for this was that if the groom found his bride to not be a virgin, and wished to complain against her, he could because there would be time before shabbat. Thursday did not allow the time needed, and, of course, no one could expect a widow to be a virgin. 
Further, there would be these water jars because of the wine. Water was used extensively when wine was on the scene. Drunkenness was never acceptable by Torah law, though any who drink will tell you that they feel some effect with the first drink, therefore the cheaper wine was brought out after the better wine had done its job and made the festivities a bit on the tipsy side.
Wine, however, was watered down in all cases---though I would expect that any who could afford or were less scrupulous with the Law, probably did not water down the wine. On the other hand, it is known that watering down wine today enhances the flavor of the wine ( New York Times ). 
Wine watered down stretched all the further, and it had some benefits for the water. The low alcohol level killed off most bacteria, at a ratio of 20:1 or 4:1, depending on the account, allowing the non-so-clean water to be cleaner yet. While the Jews followed the laws on what water to use, this process still would assist in maintaining the health of the water. (Wine Speculator; ) (Wine In The Ancient World  )( Fermented or Unfermented)
 Barker makes the point that the translation of alcohol in the Word comes from the word oinos, which means "grape juice" or "wine", depending on which the person was speaking on. Ancient articles from Roman times, including Pliny the Elder, describe in great detail how to store grape juice to NOT ferment, as well as preventing too much fermentation from occurring in wines kept. ( Wine in Ancient World )(Wine History,( Forum )
It was consider a social disaster to run out of wine at a wedding. So Jesus' mother goes to Him, which suggests that she was likely a relative of the bride or groom, and states that they have no more wine. Disaster! ( GotQuestions )
Christ's answer seems, perhaps, rude. "Woman" in today's society is often a putdown, a dehumanizing statement. It is more like saying "Madam" in this culture and time. It is a title, it is honorable, and it is certainly not a rude statement. His question of what does this have to do with me and then that His hour has not come might refer to the timeline of His public works--since His active work begins in the next section.(GotQuestions  ) Mack suggests that His question and His answer have a way of separating Himself away as a son, that He must leave all behind.( Mack ) Mary is really only mentioned a few times during the Gospels--the times I can remember are the beginning, the wedding scene here, in Matt 12.46-50, when Jesus is told His mother and brothers want to see Him (thinking He had lost His mind), and at His death, when He left John to care for His mother. 
The large washing jars were important to Jewish culture--everything demanded cleanliness. Jews were required to wash before meals, wash dishes, and in general be clean. Much as Christ took over the servant's job and washed the feet of His disciples, so did everyone wash the dirt, dust and mud from their feet. Sandals, which were little more than leather tied to one's foot, were not much protection against dust and mud. Then, before meals, between courses (!) one would wash their hands. 
Christ ordered the jars filled, then to take a dipper to the master of the banquet. I, like Mack, find this humorous. It was common in pagan temples to use "trick" jars to turn water into wine, so Christ doing so, without touching the jars, is amazing and also quite funny. Somewhat like Aaron's snake eating the Egyptians' sorcerers' snakes. (Mack  ) 
The wine Christ made was taken to the master of the banquet, who called to the Groom (as you recall, his family is required to have enough wine for the wedding banquet) and praised the wine's flavor. 
This is the first of seven miracles listed in John's writings.