Another way to say this is man is justified by faith from which works will flow, i.e. not lip service faith, but full blown "all in" faith. When God saves us, He puts us spiritually in Christ and indwells us with the Holy Spirit, and our lives change as we exhibit the fruit of the Spirit.
But what if we profess we believe in Christ, but God does not credit as righteousness, and put us in Christ. One way to know is at communion, where we examine ourselves to see if we are of the faith. Do we still love Jesus more than anything else, and can we discern the fruit of the Spirit in our lives? If the answer is yes, eat the bread and drink the cup, in remembrance of what Christ has done for us!
Thus the idea is we are justified, i.e. placed in Christ and washed with His Blood, provided God looks into our heart and discerns we are all in for Christ, holding nothing back. So when you see "dead" faith, it is a superficial faith from which works does not flow.
In summary before we are saved, all our works are as filthy rags, and these do not earn or merit salvation or contribute to our salvation. But when God credits our "faith alone" as righteousness, it is full blown faith from which works will flow, thus we are justified by faithful faith, or a faith that will be accompanied with works.
So when we show our "faith" to ourselves to see if we are of the faith, we look for faith, i.e. love of Christ, plus works, we are striving to follow Christ. This is because "faith" without works is dead, i.e. not the faith God credits as righteousness.
