The word translated “souls” in this verse is the Greek word “psuche.” Psuche is where we get the English word psyche and is translated half the time “life” and half the time “soul”. They are the same thing in the Bible.
The word translated “save” is the Greek word “sozo.” It is sometimes translated “heal” or “make whole”. This is because “sozo” means “something is delivered from something.” The context tells us what is being delivered from what. If a sick person is delivered from illness, they are “sozo” or “saved” from sickness. Which is why the translators might render “sozo” “healed” or “made whole.”
So how do we save (“sozo”) our lives (“psuche”) from wickedness and filthiness? We save our “lives” (or “psuche”) from wickedness and filthiness by putting it aside. A bit of a paradox. Why does the Bible tell us to “put aside our wickedness?” Why not “avoid” or “steer clear from?”
The preceding verses in James 1 tell us. The reason we are told to put aside wickedness is because the wickedness is within us. In our flesh. Our old nature is still with us. That is what tempts us. It will dominate if we don’t set it aside.
Being able to listen to people requires us to set aside self for a moment so we can see as they see. This skill translates to hearing what the Bible teaches. Listening to the Spirit. And this word, implanted, “saves our psuche” from the adverse consequences of following the desires of the flesh.