What does $|w|$ mean in the statement " $|w|$ where $w \in L \subset \Sigma^*$"?
Usually, $\Sigma^*$ denotes the set of all strings obtainable from an alphabet $\Sigma$.

Most probably, $L$ is a language and $w$ is a word. A language is a subset of the alphabet $\Sigma^*$, thus $L \subset \Sigma^*$.

A word, on the other hand, is a single string obtained from the language $L$.

As an example:

$\Sigma = \{0,1\}$
$\Sigma^* = \{0, 01, 10, 11, 100, 101, \dots, 1011001001, \dots\}$
$L \gets$ all strings containing an even number of zeroes
$w \gets 100010$

And $|w|$ is probably the length of $w$.