What does it mean that the gospel is the power of God for salvation?
The gospel is the power of God unto salvation because, like an outside charge reviving a dead battery, it infuses life from God's source. It saves everyone who believes, not by joining a church, baptism, communion, tithing, or good works, since those are not the saving power.
Les explains from Romans 1:16 that Paul was not ashamed of the gospel of Christ because the gospel itself is the power of God unto salvation. To illustrate, Les compares it to a dead car battery: when jump cables from a charged battery or a generator bring outside power into it, the battery receives life from another source. Likewise, the gospel is that generating power from God. Les stresses that salvation is not by joining the Church, getting baptized, taking communion, tithing, or doing good works; those may have their rightful place, but they have nothing to do with salvation. He also says believing is not merely saying Christ died for me, but totally entrusting one's eternal destiny to the Word of God and the power of the gospel.
For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek.