"Jews demand miraculous signs and Greeks look for wisdom, but we preach Christ crucified: a stumbling block to Jews and foolishness to Gentiles," NIV translation
Both Jews and Greeks wanted God to show Himself but they wanted it on their terms. When God showed up by sending His Son to the cross, it was not what they expected and so many rejected God. The same type of thing happens even more today in that many people want to have God's presence but they want it on their own terms. Jesus said that He was the only way and it was proven true by His resurrection.
"but to those whom God has called, both Jews and Greeks, Christ the power of God and the wisdom of God. For the foolishness of God is wiser than man's wisdom, and the weakness of God is stronger than man's strength." NIV translation
As Christians, we understand that there was no other way to restore the broken relationship between ourselves and God except for Jesus to suffer and die on the cross. Although the world sees those events as weakness, we see God's power on display as He raised Jesus from the dead.
"Brothers, think of what you were when you were called. Not many of you were wise by human standards; not many were influential; not many were of noble birth. But God chose the foolish things of the world to shame the wise; God chose the weak things of the world to shame the strong." NIV translation
The wisdom of the world says that, in order to be heard, you must use those that hold the keys to power such as politicians and those with money. The wisdom of God says take a group of common men that are willing to be used by Him and change the world. That is what happened with Jesus and the apostles. Most of them were common fishermen and Jesus was the son of a carpenter. But, with God, they were used to change the world.
The same is true today in that God still uses the common people more than the well educated or the rich. There are two main reasons for this and the first is that "common people" are more willing to listen and obey the Lord. The rich and powerful get so caught up in themselves that they often do not have the time or the desire to listen to the Lord. The second reason is that using the "weak things" brings greater glory to God as people can see that it is only possible with God.
"He chose the lowly things of this world and the despised things - and the things that are not - to nullify the things that are, so that no one may boast before him." NIV translation
God usually uses the lower class people of the world to carry out His work. He does this so that people will see that it is only possible through the power of God. Through these "lowly things" people will see what faith in God can accomplish.
"It is because of him that you are in Christ Jesus, who has become for us wisdom from God - that is, our righteousness, holiness and redemption. Therefore, as it is written: 'Let him who boasts boast in the Lord.'" NIV translation
None of us came to faith in Jesus on our own. We are in Christ because God called us to Himself and He has become our wisdom. Though it does not make sense to most of the people in the world, we are made right with God through Jesus. Since, it had nothing to do with our own work, the only thing that we have to brag about is God's love and mercy.