$x ||= 0; translates to $x = $x || 0;. You might use this to assign a default value to a variable when you didn't want to test whether or not the variable is defined. $x stays the same if $x is defined and is not equal to zero. If it is equal to zero, it falls through the "or" (||) and sets it to zero.

So the only time this changes the value of $x is when $x is undefined. That's a short-hand way of writing:

$x = 0 if (!defined $x);