What does -z mean in Bash?

The expression -z string is true if the length of string is zero.

test -z returns true if the parameter is empty (see man sh or man test).

-z

string is null, that is, has zero length

String=''   # Zero-length ("null") string variable.

if [ -z "$String" ]
then
  echo "\$String is null."
else
  echo "\$String is NOT null."
fi     # $String is null.

-z string True if the string is null (an empty string)