create table file_multi (id int NOT NULL AUTO_INCREMENT, filename varchar(255), PRIMARY KEY(id));

<form action="file_upload.php" name="upload_form" method="POST" enctype="multipart/form-data">
    Файлы:<br />
    <input type="file" name="file[]" multiple />
    <input type="submit" value="Отправить" />
</form>

<?php
$host = "localhost";
$username = "user";
$password = "pass";
$dbname = "dbname";
$conn = new mysqli($host, $username, $password, $dbname);
if ($conn->connect_error) {
    die("Connection failed: " . $conn->connect_error);
}
foreach ($_FILES['file']['name'] as $filename) {
    $sql = "insert into file_multi values(NULL, "{$filename}")";
    $conn->query($sql);
}
$conn->close();