This is a flat sign.
When a flat sign is placed before a note on the staff, it means that you play the key immediately to its left. This key may be either black or white. E.g., the note B flat (written as Bb) is shown on the staff, as follows.
To play the note Bb, play the black key immediately to the left of the B note (white key), as shown on the diagram.
To see which finger you should use to play the Bb note, look at the fingering numbers written above the note in each song.
As with the sharp sign in the previous lesson, instead of writing a flat sign before every Bb note on the staff, it is easier to write just one flat sign after the treble clef. This means that all the B notes on the staff are played as Bb, even though there is no flat sign placed before them.