How can the use of hidden input fields in PHP forms be utilized for passing values between client-side and server-side scripts?

Hidden input fields in PHP forms can be utilized to pass values between client-side and server-side scripts by including them in the form with the attribute type="hidden". These hidden fields are not visible to users but can store values that can be submitted along with the form data to the server. This allows for passing data from the client-side to the server-side scripts without displaying it to the user.

```php
<form method="post" action="process_form.php">
    <input type="hidden" name="hidden_field" value="hidden_value">
    <!-- other form fields here -->
    <input type="submit" value="Submit">
</form>
```

In the above code snippet, a hidden input field named "hidden_field" is included in the form with the value "hidden_value". When the form is submitted, this hidden value can be accessed in the server-side script (process_form.php) using $_POST['hidden_field'].