What does the Cyrillic letter "ь" do to the consonant before it?

I have seen so many Latinized Russian words with an apostrophe at the end. When transliterated into Cyrillic, said apostrophe transforms into a "ь". But what does it really do to the consonant before it? Does it just change the consonant or does t also change the sound of different parts of the word? Please help :)