To reconcile a payment with an invoice means, if you receive a payment from a customer you match it to the invoice that they are paying. You reconcile the payment with the corresponding invoice.
In Odoo, an invoice is considered to be paid when the associated accounting entry has been reconciled with the payment entries. If there has not been a reconciliation, the invoice will remain in the Open state until you have entered the payment.
A typical journal entry generated from payment will look like as follows: 
You can now go through every transaction and reconcile them or you can mass reconcile with instructions at the bottom.
After reconciling the items in the sheet, the related invoice will now display “You have outstanding payments for this customer. You can reconcile them to pay this invoice. “
