Magento2 checkout form: How to display placeholder attribute value in fields?

Standard way,

Copy all html files from vendor/magento/module-ui/view/frontend/web/templates/form/element/ at app/design/frontend/<Vendor>/<theme>/Magento_Ui/web/templates/form/element/

Then change all Change placeholder: placeholder to placeholder: label as mention by Akis Verillis.

Now you need to deploy the static files by below code:

 php bin/magento setup:static-content:deploy

And see the magic.

Note: If you have checkout from github then try copy from

/app/code/Magento/Ui/view/base/web/templates/form/element/

Change placeholder: placeholder to placeholder: label

The answer is in Magneto 2 documentation now: http://devdocs.magento.com/guides/v2.0/howdoi/checkout/checkout_edit_form.html The templates are the ones mentioned in previous answers. The templates from magento-ui module are used in other places than checkout.

In your custom module directory, create a new /view/frontend/layout/checkout_index_index.xml file. In this file, add content similar to the following:

...
<referenceBlock name="checkout.root">
<arguments>
    <argument name="jsLayout" xsi:type="array">
        ...
        <item name="shippingAddress" xsi:type="array">
            <item name="children" xsi:type="array">
                <!-- The name of the form the field belongs to -->
                <item name="shipping-address-fieldset" xsi:type="array">
                    <item name="children" xsi:type="array">
                        <!-- the field you are customizing -->
                        <item name="telephone" xsi:type="array">
                            <item name="config" xsi:type="array">
                                <!-- Assigning a new template -->
                                <item name="elementTmpl" xsi:type="string">%Vendor_Module%/form/element/%your_template%</item>

%Vendor_Module%/form/element/%your_template% path is [your theme dir]/Vendor_Module/web/template/form/element/your_template.html

Clear browser cache too beside: Delete all files in the pub/static/frontend and var/view_preprocessing directories.