Living water is a reference to the Holy Spirit.
In the last day, that great day of the feast, Jesus stood and cried, saying, If any man thirst, let him come unto me, and drink. He that believeth on me, as the scripture hath said, out of his belly shall flow rivers of living water. (But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.)
- John 7:37-39 (KJV)
That's what it means to be baptized by the Holy Spirit.
Jesus answered and said to her, Whoever drinks of this water will thirst again, but whoever drinks of the water that I shall give him will never thirst. But the water that I shall give him will become in him a fountain of water springing up into everlasting life.
- John 4:13-14 (KJV)
There are only two references to living water in the Bible.