Paul certainly was not preaching about the piece of wood that Jesus died on. The word “cross” is being used to refer to the work that Jesus accomplished for us through His substitutionary death and resurrection. Therefore, this is referring to the atonement Christ made for us (Matthew 26:2).

However, the term “cross” here, as well as many other places in Scripture, has an even more specific meaning referring to the method that God used to bring us salvation. It particularly alludes to the fact that salvation is a gift to be received; it is not a prize to be earned. Jesus paid it all, even our penalty of death for the sins that we had committed.

There is nothing left for us to do except believe the good news. So Paul’s invocation of the cross is referring to the fact that salvation cannot be earned; it’s a gift. This was his favorite theme, and this was what he declared makes no sense to unbelievers. It takes a special revelation to understand salvation by grace through faith (1 Corinthians 2:14).

Therefore, when Paul referred to the cross of Christ, he was referring to the grace of God as the method of salvation. Indeed, in this verse he stated that the cross of Christ is the power of God. This is the same phraseology that was used in Romans 1:16 to refer to the Gospel of grace (see note 1 at Romans 1:16).

Note 2
The Greek word that was translated “perish” is the word “APOLLUMI,” and it means “to destroy fully (reflexively, to perish, or lose)” (Strong’s Concordance). This same word was translated “lost” in 2 Corinthians 4:3, “But if our gospel be hid, it is hid to them that are lost.” Therefore, Paul was referring to those who have not been born again through faith in Christ as their Savior.

Note 3
This verse is a continuation of Paul’s reasoning in the previous verses. Paul had just made it clear that Christ wasn’t divided, so the Corinthian believers shouldn’t be divided either. He mentioned that the Lord didn’t send him to preach peripheral issues like water baptism (1 Corinthians 1:17) but to stick to the Gospel of the grace of God that is summarized by Jesus’ death on the cross.

Here he continued to expound on the power of the grace of God  and he contrasted simple faith in God’s grace with intellectualism. He was doing this to counter the strife and division that he had rebuked in the previous verses. This is because all strife is rooted in pride (see note 11 at Acts 20:30). These divisions came because people exalted man’s wisdom above God’s wisdom.

Promoting man’s wisdom at the expense of simple faith in the Word of God is pride and is at the root of all division. Therefore, Paul made a rather lengthy declaration about the wisdom of God being far superior to the wisdom of man (1 Corinthians 1:18-3:23).

a [preaching] Greek: logos (GSN-<G3056>), word (note, Acts 1:1).

b [perish] Greek: apollumi (GSN-<G622>), note, Mt. 10:28.

c [foolishness] Greek: moria (GSN-<G3472>), silly, absurd, foolish. Only in 1Cor. 1:18,21,23; 2:14; 3:19.

d [us which are saved] For us who are being saved, salvation has a present and future aspect (Rom. 13:11; Php. 2:12; 1Th. 5:8-9; 2Tim. 1:9; 3:15; 4:18; 1Pet. 1:5).

e [it is the power of God] The preaching of Christ, the gospel, and the cross saves the souls of people (1Cor. 1:18-24; Rom. 1:16).
Dake's Annotated Reference Bible.