The purpose of billing plan is to enable the students that are added in the same class to pay a different rate. For example, there can be 3 billing plans in a class - Monthly, Termly, Paid trial. Once it is set up, the system can auto-generate the first invoice with the correct invoice items just by selecting the appropriate billing plan. This offers greater flexibility as you don't have to create and manage multiple classes - where one class is created for each type of pricing.
Billing plans can be used for all types of invoicing - from recurring invoicing (monthly or termly invoicing) to one-time invoicing (paid trial and holiday classes).