I don’t know what practice you’re pursuing, and I don’t know how other forms of Buddhist practice deal with this “blankness”, but in Zen there’s no special significance attached to it. It’s just one of many mind-states that arise in meditation and, as with all other states, it’s neither good nor bad; it’s simply what has arisen at the moment.
It’s dealt with as any other state is dealt with: you acknowledge it, neither latching onto it nor pushing it away, but then you return your attention to the focal point of your practice and just leave the state alone. Like all things that arise, it will also leave. It’s coming and going are of no concern, and are irrelevant to the practice.
The blankness you’re talking about has something of a bad reputation among Zen practitioners; it’s been called the “dead-void” and the “cave of the devils” because it can have a certain seductive quality that can easily derail you from your practice (e.g. this from Hsu Yun: “You should know that there is another error into which a Zen practitioner may easily fall, that is to meditate idly and make his mind deadly dull in utter torpidity. This is th worst error of all”) That blankness is such a novel sensation, and it carries a sense of relief from the normal whirlwind of thoughts, so the temptation is to hang out there and relish the blankness, as if it were the destination or the point of practice. For as long as there has been Zen practice, masters have been warning their students not to get seduced by this “cave”, but to just keep working through the state.
Just to clarify a misconception in your previous comment, “zazen” does not refer to this blankness.