Answer "is it still under warranty?" from the serial number.
A customer says their unit is covered. Without a record, you either take their word for it or spend an afternoon digging through order history. With one, you search the serial number and see when it shipped, on which order, and to whom.
What the record gives your support team.
The serial number is the key to all of it. That is why it is worth scanning each unit as it goes in the box.
The ship date for that exact unit
Warranty terms vary. Some run from the purchase date, some from the day the unit shipped, some from the date it was made. You already have the purchase date on the order, and a production date comes through in the barcode when the label carries one.
The ship date for one specific serial number is the one you cannot get any other way. It is on the record from the day you packed it.
The customer it went to
Useful when the person contacting you is not the person who bought it. A gift, a resale, or a second location of the same business.
The rest of that shipment
If a whole order is failing, the other serial numbers on it are right there, so you can get ahead of the next three tickets.
Repeat repairs
A unit that comes back twice is a different problem from two customers with the same complaint. The serial number tells you which one you have.
Start recording on the next shipment.
Connect your store, scan one order, and look at the record. About five minutes to set up, and nothing to pay for thirty days.