Adding inside wp-plugin jQuery script that receives JSON-formatted data, generated by php-function inside this plugin

Have a read of AJAX in Plugins, then see if you can adapt this code to what Highcharts is wanting:

add_action('wp_ajax_wpse_77392_get_json', 'wpse_77392_get_json');
add_action('wp_ajax_nopriv_wpse_77392_get_json', 'wpse_77392_get_json');

function wpse_77392_get_json() {
    global $wpdb;

    $sql = "
        SELECT `date`,`value`
        FROM {$wpdb->prefix}table_name
        WHERE `date` BETWEEN '2011' AND '2012'
        ORDER BY `date` ASC;
    ";

    $results = $wpdb->get_results($sql);
    $json = json_encode($results);

    header('Content-type: application/json');
    echo $json;
    exit;
}