Folio is an industry codeword for the collection of charges. 

A folio is created for the guest account. You can post charges and payments for a specific guest to a folio that can be assigned to the guest or to the company. 

Think of it like a folder of all the bills a customer may have at the hotel such as:

You can have multiple folios in a booking and can split or pass charges between them.
Folio's are usually found in the booking and generally they would be for the customer. But there are some cases where you would want the folios to be assigned to another person or a company.

In this example the main folio would be under the company name and address and another folio is made to contain the guests incidentals like food & drink or extra nights.

This is very similar to the company example but the guest has paid both, the folio with the room charges is made to TA and is not to be shown to the guest. If the guest has other charges we have a separate folio for those charges.

Folios can be turned into Invoices and sent to the guest/company. And invoices can be made into receipts if full payment has been made. Receipt status is a final status and no amendments are allowed after the receipt has been issued. You would need to credit the receipt and amend the new folio.