Sometimes, you might email an invoice to a client, but it does not get marked as Posted after emailing.
Marking emailed invoices as Posted helps to identify which invoices have been emailed out, as the invoices are marked with a blue line on the left in the list view. The blue line acts as an indicator to keep you from emailing the invoice twice. Core marks the invoices as Posted only if you email them to the client or client contact without previewing them. That is, if you select the invoices in the Invoices screen and then click Actions > Email > Client or Client Contact without previewing them in the subsequent prompt. You can also mark the invoices as posted manually using Actions > Batch Update. On the Batch Update screen, set Posted Status to Mark as Posted and Save.
Invoices also get marked as posted by other means, e.g., if a payment is made on them. This is not the best way to keep track of invoices that you have emailed. You should rather use the Last Emailed On column in the Invoices screen to keep track of it. Check out this article for more details on invoices.