What does the statement |b|=7

mean?

It means b=±7, that is b=-7 and + 7. Because it is within absolute values brackets it can be either positive or negative as long as its magnitude is equal to 7 ...

The absolute value of b is equal to 7. Absolute value means the distance from zero. In simple terms, the positive version of the number. B could be 7 or - 7, since both will be equal to 7 when you take their absolute value.