The miracle at the wedding in Cana of Galilee is recorded in John 2:1-11. When the wine ran out during the celebration, Jesus' mother informed him of the situation. Jesus then instructed the servants to fill six stone jars with water and draw some out to take to the master of the banquet, who found it had become excellent wine.
The Gospel of John explicitly states the purpose of this miracle in verse 11: "This, the first of his signs, Jesus did at Cana in Galilee, and manifested his glory. And his disciples believed in him." The miracle served as a revelation of Jesus' divine nature and power, leading his disciples to place their faith in him.
While Jesus did respond to his mother's concern and did meet a practical need at the wedding, these were not the primary purpose John recorded. The theological significance was the manifestation of divine glory and the strengthening of the disciples' faith. Supporting the institution of marriage, though a worthy purpose, is not stated in the text as the reason for the miracle.