What is a hyphen beside a shell variable

It's all explained in the Shell Parameter Expansion section of the manual:

${parameter:-word}

If parameter is unset or null, the expansion of word is substituted. Otherwise, the value of parameter is substituted.

Just before this there is:

Omitting the colon results in a test only for a parameter that is unset.

So:

${X-stuff}

expands to:

• The expansion of $X if X is set
• stuff if X is unset.

Try it:

$ unset X
$ echo "${X-stuff}"
stuff
$ X=
$ echo "${X-stuff}"

$ X=hello
$ echo "${X-stuff}"
hello
$

Now your expansion is

${X-}

so you guess that it expands to the expansion of $X if X is set, and to the null string if X is unset.

Why would you want to do this? to me it seems that this is a workaround the set -u:

$ set -u
$ unset X
$ echo "$X"
bash: X: unbound variable
$ echo "${X-}"

$

Finally, your test

if [ -z "${X-}" ]

(note the quotes, they are mandatory) tests whether X is nil (regardless of X being set or not, even if set -u is used).