Source: Computer Organization and Design: The Hardware/software Interface, David A. Patterson,John L. Hennessy
It doesn't seem as the author is using leading $0$ like leading $1$ in a matrix.
What does leading $0s$ in a number in scientific notation mean?
"Leading zeroes" are simply zeroes that appear at the beginning of the digit sequence, with no nonzero digits before them.
The text you quote seems to be leading up to an explanation of floating-point representations in computers, which generally have a format such as $$ \#.\#\#\#\#\#\times 10^{\pm\#\#} $$ with a fixed amount of space reserved for the digits of each part -- except that the base in actual computer representations is two rather than ten and the digits are bits!
If you're using such a representation, if you want to represent a very small positive number such as $10^{-103}$ you can't write $$ 1.00000\times 10^{-103} $$ because the representation does not have room for three digits in the exponent. But there is room to write $$ 0.00010\times 10^{-99} $$ where there are 4 leading zeroes in the "0.00010" part. This denormalized representation gives lower relative precision than normalized representations, so it is only used if it is the only way to represent numbers in the relevant range -- that is, denormalized representations should only be used when the exponent is the smallest possible.