Shlomo's public spectacle in Givon is essentially his announcement of his initiative to transfer the altar to Jerusalem and eventually build the Mikdash there. He  offers sacrifices on the central altar at Givon, but then immediately travels to Jerusalem to offer sacrifices there.
Shlomo's request for wisdom is followed by the famous case of his judgement. The story has two powerful messages: random people had access to the highest authority in the land and Shlomo sought to apply justice to the entire nation, and not simply to the upper classes.

Courtesy of the Virtual Beit Midrash, Yeshivat Har Etzion