The cross of Christ means God is committed to bringing sinners to become saints so much that to free the believing sinners from persistently sinning He provided a sacrifice so they can put their sins behind them knowing God is doing the same (and can rightly do the same). Once this truth is known to a believer in Christ who still struggles with a persistent sin but holds to Christ's teachings (with a mind committed to fully obeying them), the believer is animated by the hope that God will provide a way out and Christ will work powerfully to free them. So their heart is opened and the Holy Spirit enters and truth enters and the power of God teaches and enables them to put aside that sin and practise right behaviour instead. It is the truth of the cross of Christ that facilitates this by giving hope that their sin can surely be dealt with and God will help and has paid their debt to allow this freedom.
