Subscriptions in Beacon are a record showing recurring payments. They are a way of helping you see how much money you might expect to have coming in. Whilst they are related to payments, this won't replace a payment record. If someone has had a monthly subscription of £10 for the last year then you would have the subscription with 12 payments for £10 pointing to it (remember our crime board).
You can read more about subscriptions and how they relate to payments here.
Subscriptions are also used to automate standing orders.