Hard and Soft Sign

Here are the technical details:

The "soft sign", , indicates that you should palatalize the preceding consonant. That is, you touch your tongue to the hard palate (the roof your mouth near your teeth). This adds a sort of "y" sound to the consonant.

The "hard sign", , used to be used primarily to indicate that you should not palatalize the consonant. Nowadays, it has the main purpose of forcing a syllable break.

You can hear the difference between a soft consonant and a hard consonant, as in the American English "do" and the British English "dew."

There are a few words where the presence or absence of a soft sign changes the meaning of a word. For example,

means "corner", but means "coal".

Again, don't worry about this - the context will make your usage clear. Given a choice between sentences that translate to:

The bank is around the corner.
The bank is around the coal.

a native Russian will figure out the correct meaning even if you pronounce it incorrectly.

The Last Two