The services or resources you sell to your customers are organized into plans. A subscription is basically a permission to use the services or resources for a particular period of time.
Subscriptions also serve as a connection point in Business Manager. Invoices are tied to subscriptions. So are add-ons. A customer may stay the same, but they may have different subscriptions, and thus different add-ons and invoices, at various times in their life cycle. Subscription to a plan is a prerequisite for billing a customer. You cannot bill a customer unless they have at least one subscription tied to their account.
Business Manager handles subscriptions in two broad categories: domain subscriptions and all others. Domains subscriptions are created when a customer either purchases or transfers a domain through Business Manager.