As God's people, we need to be convinced that our faith in the Lord Jesus Christ, His death, burial, and resurrection, are how we should live! A believer we have to have a conviction of things hoped for, so that we can live accordingly.
Paul had a conviction about the Gospel! He knew it was the power of God unto salvation to everyone who believes! His final comments to the church at Rome shows that he is convinced that this message of salvation needs to and will go forth!