What this subnetting restriction means
Since each place in a binary number is a power of two, the binary expansion of $2^k$ for any $k$ will be a 1 followed by $k$ zeroes.  Examples:

$$1 = 2^0 = 1$$ 
$$16 = 2^4 = 1\underbrace{0000}_{4\ zeroes}$$
$$512 = 2^9 = 1\underbrace{000000000}_{9\ zeroes}$$

Multiplying a number that ends in zeroes by another number (integer) produces at least that many trailing zeroes.  So any number divisible by a number ending in $k$ zeroes has to end in at least $k$ zeroes.