Depending on whether you are looking at the Veracross (VCX) side or Accounting (VCA) side of your database, the "Recieves Invoices" flag on a relationship record has different funcitonality.
On the VCX side, this flag has no functionality other than it can be pulled into queries and queried upon.
On the VCA side, it is typically used in situations where parents are divorced. The student's residing household is billed, which means all invoices are addressed to the student's household address. In cases where one parent no longer lives in the same household, they will not receive an invoice, nor will they be able to see it in the parent portal (if your school is displaying invoices in the portal). So, if the non-resident parent needs to receive a copy of the invoice or see it in the portal, they need the "Receives Invoices" flag checked in the related person record.
This flag should only be set for non-resident parents/guardians and not for resident parents.