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Customers can be set up so that payments auto apply to invoices, or the lab can manually apply payments against specific invoices.
Auto apply would be used when a customer uses a "balance-foward" method, where they pay an amount (based on their statement), and the amount is applied against invoices, starting with the oldest invoice that has any balance due, until the payment is exhausted. This is what most customers will use for most labs.
Auto apply would not be used when a customer pays on a "per invoice" basis (also sometimes called open-item). In this case, the customer will indicate (on the statement or cheque stub) which specific invoices they are paying, and will require the lab to allocate the payment against those specific invoices.
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Taking the same scenario as above, but with the customer configured NOT to automatically apply payments,let's assume the customer sends in a cheque for $123.70, with instructions to pay invoices 805665 and 875102. Perhaps there is a dispute about the charge for 874555, and that invoice is omitted from the payment instructions. 
When the $123.70 payment is entered, nothing is automatically applied, and the "Remaining" field shows the amount of the payment remaining to be allocated. The lab can go to the "disc taken" column of the first invoice, and press enter - since the payment date is beyond the discount date for that invoice, no discount is applied (the lab can over-ride this if desired by entering in a discount amount). Tabbing to the payment entry for that invoice, and pressing enter, will default the payment to the full amount of the invoice:
Let's skip invoice 874555, since it wasn't listed on the cheque stub, and go to 875102, which was listed. When we press enter on the discount taken column, the eligible discount will show, since the payment has come in before the discount date for this particular invoice. The payment will default to the balance owing for the invoice (which is also the balance left on the payment, since the customer paid the invoices in full):
When the statement is run for this customer for February, it will show the invoices that were fully paid, and will show eligible discount only for the invoice in February not yet paid. No eligible discount would be shown for invoice 874555, because the payment wasn't made before the discount date (10 Feb 2017):
Deleting A Payment
If a payment had been entered in error (perhaps associated with the wrong account), it can be deleted. When a payment is selected for deletion, the lab will be warned:
Any invoices that were formerly marked as reconciled (fully paid), will be available for payment again. If a payment is deleted for a period in which a statement had already been generated for a customer, the statement for that period should be re-created and re-sent to the customer.