What does it mean to me?"
Well, I feel that it means that the wisdom of men is nothing, or, earthly wisdom is foolishness. That trusting in God and what he did for us (sending a savior) is true wisdom.
It's hard to get a complete grasp of the intent of this one scripture without a little more explanation of God's word.
1 Corinthians 1:19 For it is written:
“I will destroy the wisdom of the wise,
And bring to nothing the understanding of the prudent.”
20 Where is the wise? Where is the scribe? Where is the disputer of this age? Has not God made foolish the wisdom of this world? 21 For since, in the wisdom of God, the world through wisdom did not know God, it pleased God through the foolishness of the message preached to save those who believe. 22 For Jews request a sign, and Greeks seek after wisdom; 23 but we preach Christ crucified, to the Jews a stumbling block and to the Greeks foolishness, 24 but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God. 25 Because the foolishness of God is wiser than men, and the weakness of God is stronger than men.
Just like when Jesus finally died on the cross and the curtain was split that separated the people from the most holy place in the temple. (ref. Matthew 27:51)
Those of that day, who were the "most wise" were now part of the body and family of Christ - if they chose to be. It no longer mattered what you knew, or in other terms, how smart you were - if you believed, in your heart and soul, in Jesus as your savior that you had the grace of God and eternal salvation.
That's what it means to me anyway.