The phrase "living waters" or its singular is found only eight times in the King James Bible. Both the Hebrew and Greek words translated as "living" (Strong's #H2416, #G2198) in these phrases mean something that is alive, fresh or flowing.
Jesus, in 29 A.D., was in Jerusalem to keep the Feast of Tabernacles and the Last Great Day. The High Priest, in the morning of each day, carried out a tradition known as the water pouring ceremony. It entailed him pouring out, at the temple, a golden vessel filled with the precious liquid collected from the Pool of Siloam. The pool was fed by Jerusalem's Gihon Springs, considered the quintessential source of living water.
On the Last Great Day, a high holy day, Jesus made a startling and bold public announcement. While the above ceremony was taking place (or immediately after it) he loudly cried the following for all those in the temple to hear.
If anyone thirsts, let him come to Me and drink. The one who believes in Me, as the scripture has said, out of his belly shall flow rivers of living water (John 7:37 - 38, HBFV throughout).
Background
Israel had access to three primary sources of drinkable water. The first, and least desirable, was through cisterns utilized to store rainwater. Varying in size, they trapped the valuable liquid from roofs, tunnels and courtyards. Private, as well as public cisterns, were common (2Kings 18:31, Proverbs 5:15). These storage areas, however, were prone to breakage (Jeremiah 2:13), stagnation and contamination.
The second source of water was wells. They were generally more desirable than cisterns, as their source was deep groundwater and springs that reliably replenished themselves. Their value, however, made them a flashpoint for conflicts (Genesis 21:25 - 30, 26:19 - 22, 2Kings 3:19). The third and most prized source was from rivers, brooks, streams or springs that bubbled to the surface. These were considered sources of living water as they were considered fresh and constantly moving.
Symbolism
The Apostle John reveals the meaning of Jesus' statement.
But this He spoke concerning the Spirit, which those who believed in Him would soon receive . . . (John 7:39).
Humans must first come to Jesus before they can "drink" of living water. Even as the Gihon Springs was Jerusalem's only supply of fresh water in antiquity, so Jesus is the only source through whom the world can receive eternal salvation (Acts 4:10 - 12). He makes it possible for us, upon repentance, to receive God's spirit.
Once dwelling in a person, the Holy Spirit leads them to develop the same kind of character as God. As they mature, their lives become like lights promoting God's way (Matthew 5:14 - 16) and like rivers spreading his truth. The fullness of being a source of "rivers of living water," however, will occur after a Christian is resurrected, given eternal life, and enters God's family.
It was also no accident that Christ waited to the Last Great Day to make his announcement! This High Holy Day symbolizes the Great White Throne Judgment (Revelation 20:11 - 13). It will be a time, after the Millennium, when all those up to the Lord's Second Coming who never received a full chance at salvation will be brought back to life. They will then be given a chance to repent and partake of God's spirit. Anyone who "thirsts" at that time will have the opportunity to live forever in God's Kingdom (Revelation 22:1 - 2)!
Literal meaning
A literal manifestation of the miraculous waters Jesus spoke of will also appear in the near future!
An east-west river of living waters, which will spring up from Jerusalem, will exist after Jesus' return. Half of this river will flow toward the Dead Sea. This miraculous liquid, possibly following the valley created by the Mount of Olives splitting in two (Zechariah 14:3 - 4, 8), will heal the Dead Sea of its saltiness that currently makes life impossible.
. . . there where the rivers go, every thing shall live. And there shall be very many fish because these waters shall come there. And they shall be healed. And all shall live where the river goes. And it will be, the fishermen shall stand on it from En Gedi (Engedi is near the western shore of the Dead Sea, Ezekiel 47:9 - 10) . . .