It's just PHP, not HTML.
It parses all HTML fields with [] into an array.
So you can have
<input type="checkbox" name="food[]" value="apple" />
<input type="checkbox" name="food[]" value="pear" />
and when submitted, PHP will make $_POST['food'] an array, and you can access its elements like so:
echo $_POST['food'][0]; // would output first checkbox selected
or to see all values selected:
foreach( $_POST['food'] as $value ) {
print $value;
}
Anyhow, don't think there is a specific name for it