I would also like to know

The Payment Date is an informational field. You don't have to use it but it can be helpful.

We use it when we run our Open Invoices reports in preparation for cutting checks. We cut checks on Fridays and so, our payment dates are always a Friday. We run the Open Invoices report with a condition that the payment date is less than or equal to "upcoming Friday" so we can review which invoices we are going to pay for that week. For our subcontractor payments, we always use the 25th of the month so we can condition the Invoice by Job by that particular month we want to pay.

Hopefully, that makes sense!

I agree with Kaysong70 but thought I'd add a bit more information.  The payment date can prefill based on the setting in AP and for each vendor.  See:  https://us-kb.sage.com/portal/app/portlets/results/viewsolution.jsp?solutionid=224924450058734&page=1&position=7&q=payment%20date.  For us, we setup the payment date to coincide with whatever date a vendor will still offer a discount.  For example, some vendors offer a 1% discount if paid by the 10th of the following month.  So our vendor's settings under Terms & Defaults would be Discount Percent 1,  Discount Days 10,  Payment Days 10, Payment Days Type = Day of next month.  So during invoice entry, the Payment Date would automatically prefill and the 1% discount would automatically calculate.  Even with the automatic prefills based on the Terms and Defaults, we can override it during invoice entry because the AP Settings for Payment Date is marked as "not required". 

A vendor that does not offer a discount, may be due in 30 days from invoice date, so the Terms & Defaults on the Vendor's setup would be Payment Days 30, and Payment Days Type would be Number of days. 

So, when we do the AP - Tasks - Select Invoices to Pay, since every invoice has some payment date (or due date) entered, we can select the invoices based on the Payment Date entered on each invoice.  This is really what I think Payment Date is used for. 

Not to take away from anyone else as their answers are more informative than mine — but I have come to realize that that field is mislabeled or at the very least misleading. To me, it should be titled “Anticipated Paid Date.”  It’s nothing more than when you can anticipate paying it. It has nothing to do with then it was or will be actually paid.  

It can get confusing on canned reports as sometimes our users think it means when it was actually paid.