On the last day, that great day of the feast, Jesus stood and cried out, saying, “If anyone thirsts, let him come to Me and drink.
He who believes in Me, as the Scripture has said, out of his heart will flow rivers of living water.”
But this He spoke concerning the Spirit, whom those believing in Him would receive; for the Holy Spirit was not yet given, because Jesus was not yet glorified.
[John 7:37-39 NKJV]
On the last day ...
The last day refers here to the last day of the feast of Tabernacles, which ultimately refers to ‘the last day’, because the Feast of Tabernacles — the Feast of Dwelling In Booths — represents ‘the last day’; the end of the matter; the conclusion of the plan of God.
... that great day of the feast ...
means the feast day itself, and it is significant that Jesus returns to His metaphor “out of His heart will flow rivers of living waters”. Now we can see that He is referring to The Holy Spirit, so that not only does it respond to the verses preceding this (see ‘Where I Am You Cannot Come’), but also links the events in Chapter 7 firmly with the Feast of Tabernacles, also known as (among other names) the Feast of Ingathering.
... Jesus stood
Jesus was deliberately placing Himself as central to the meaning of the Feast; thus proclaiming that He was ‘the Lamb of God, who takes away the sin of the world’. By doing so, He is publically declaring Himself as ‘the anointed one’, The Christ. From this point onwards is the outworking of that declaration.
Whenever the insistence is on the point that God answers prayer, we are off the track. The meaning of prayer is that we get hold of God, not of the answer.