If you're trying to output something if a checkbox was checked, use:
<?php if(in_array('news', get_field('checkbox') )): ?>
<h1>News was ticked!</h1>
<?php endif; ?>
If you're trying to just display a list of the checked options, use this:
<p>Categories: <?php get_field('checkbox'); ?></p>
This will give you an array of values that you can manage with a foreach declaration. Using the_field('checkbox') will give you a comma separated string of the options that you can split up as well.
I would also suggest you go to ACF's site and go through the documentation. Most questions of this type will be answered there in decent detail, and the developer is active in his support forums as well.
EDIT: If you're wanting the list of available options output into a page for generating a dynamic query, I have just the thing. This is a piece I just built out yesterday for pulling a list of meta values from a given custom field key (using ACF). I've made it fairly generic for you. There's another chunk of JS for handling the ajax request, and a rather convoluted piece of php that outputs the resulting posts. I can't really rewrite those - the JS is standard WP forward-facing ajax call/response, and the PHP is a mess of conditional checks for the 12 different ACF fields we're displaying (2 of which are repeaters). The basics are this code here, the button onClick calls the ajax function in a separate JS file, and the php for the ajax function itself essentially sets up an array of arguments for the query, one of which is $selectedOption or $_POST['option'] as meta_value. That gets fed to a new WP_Query( $args );, which is then used in a loop, the output of which gets fed back to the js via add_action('wp_ajax_the_ajax_hook', 'fetch_option_list'); and add_action( 'wp_ajax_nopriv_the_ajax_hook', 'fetch_option_list' ); //for non logged-in users.
// Get list of meta_values for given meta_key and post_type (page, post, custom post type)
function meta_list($key = '', $type = '', $status = 'publish'){
global $wpdb;
$r = $wpdb->get_col($wpdb->prepare( "
SELECT DISTINCT pm.meta_value FROM {$wpdb->postmeta} pm
LEFT JOIN {$wpdb->posts} p ON p.ID = pm.post_id
WHERE pm.meta_key = '%s'
AND p.post_status = '%s'
AND p.post_type = '%s'
ORDER BY pm.meta_value ASC", $key, $status, $type));
return $r;
}
// ADD EG A FORM TO THE PAGE
function meta_ajax_frontend(){
$formlist = meta_list('metakey', 'posttype');
echo '<form id="optionSelect">';
echo '<select id="optionList" name="optionList">';
foreach($formlist as $fl => $val) {
echo '<option>' . $val . '</option>';
}
echo '</select>';
echo '<input name="action" type="hidden" value="the_ajax_hook" />
<input id="submit_button" value = "Search" type="button" onClick="fetch_meta();" />
</form>
<div id="meta_list">
Please select an option from the list
</div>';
}