Cyrillic hard & soft consonants -- help the newbie?

I am, verrrrrry slowly, teaching myself Russian. Up to now, the book I'm using has been pretty good with English-equivalent pronunciations for the Cyrillic alphabet, but now I've gotten to the hard and soft signs for consonants, and I'm stumped. The book has an extensive pronunciation chart, but I'm not perceiving whatever the difference is supposed to be. B as in book versus beauty; m as in my versus music; f as in four versus few -- it all sounds the same to me. I don't hear any difference in the consonants in question.

I know this is an extremely beginner-level question, but I'd like to get the basics right before I move on. Can anyone explain to me what I'm missing?