If you already have the customer details - for example, their name, email address, shipping info etc - and would like to pre-fill those fields on the cart so that they do not have to re-enter them, you can do so by providing particularly named passthrough variables (see this article for details on how to use passthrough variables).
You can use the following as the keys for passthrough variables and they will match up to the fields on your checkout page, if they exist.
Note that users can always modify this information on this page; you should rely on the information returned as part of the order info (and verified by the hash) and not the returned passthrough variables if you are using this feature.
customer_address_country - Note, this is the two digit country code; US, GB, DE, etc
The above URL would pre-fill the name field with 'Edward Mann', and the email field with 'firstname.lastname@example.org'. You should provide the fields as properly URL-encoded.