On the last and greatest day of the feast, when there'd be the maximum number of people present, Jesus stood up and made an astounding offer. But to get the best understanding of this announcement, it might help to know a little background about what the festival celebrants would've seen up to that point.
On the last day of the feast of Tabernacles, the high priest would gather the assembly in front of the temple. Together they strode down to the pool of Siloam (which will make another appearance in chapter 9), chanting psalms (probably Psalm 118 among others). At the pool the priest filled a large golden pitcher with water, then led the crowd back to the temple. At the front porch, he poured out the water to commemorate God’s provision of water in the wilderness, and publicly quoted Isaiah 12:3: “With joy you will draw water from the wells of salvation.”
Do you see why this context was so important? As this pouring out of water was fresh in their minds, holding onto God’s promise from the Old Testament that he'd pour out salvation for them “someday,” Jesus was telling them that “someday” was today. "You don’t have to wait for salvation to come. You don’t have to be thirsty anymore. I’m here. Come to me now."
My sources give me different explanations as to what Scripture Jesus was referring to in vs. 38, but the best one is that he’s paraphrasing Is. 58:11. The important thing to realize is that his promise was fulfilled on Pentecost in Acts chapter 2. John liked to give us a foreshadowing perspective. Later on he recorded that Jesus told his disciples at the Last Supper that the Spirit would be sent once he was glorified.
But let’s move beyond theology and Bible study to something a bit more practical, shall we? Are you thirsty? As a believer? Have you been trying to quench it with something other than your Savior? Why would you do something foolish like that? You know that only he can satisfy, don’t you?
Lord Jesus, I’m sorry for trying to find satisfaction in anything but you. I know better than that. Please forgive me, and let’s start over.