It is an obscure word, in Bibles only found in the King James Version, so many contemporary readers aren't even familiar with it. Modern versions of the Bible generally translate "covet," "lust," or "desire" where KJV translated concupiscence. Translators obviously felt a more general word was required, although I don't think that makes sense in Colossians 3:5 and 1 Thessalonians 4:5 (even though it does in Romans 7:8). I think the context of the Colossian and Thessalonian passages specifically includes things sexual--hence sexual arousal and desire.
Concupiscence is the very definition of how the heathen live, at least if we take our cues from the popular culture. Everything in that milieu is about sex, or more accurately, the arousal of sexual interest and its pursuit. It fills the silver screen, dominates the lyrical, and sells cars, tools, and perfume. It spills over into the church with the baptism of "romantic" love and the near universal evangelical acceptance of the cat and mouse sexual game the world is so adept at playing. I think we all need a cold shower!
Somehow Christians need to wake up from the daze we're in and realize that following Christ means not following the world. We must dare to be different, for we are a different sort in Christ. We're not called to be the versions of the worldly whose only difference from the lot is the address of our final destination. We're new creatures, with a different kind of fire, for the fire that is burning the world can only end in endless fire and is not the sort we want to share.