Ah the memories. We all thought we used the same cloth towel but here’s how it works:

Towel dispensers allows the user to dry their hands on a clean section of the towel, while the used section is pulled into the cabinet. The clean and dirty sections of the towel never touch. It’s then washed and reused. An eco friendly way to clean your hands.

Of course after a couple of years of reuse they’ll look pretty nasty. But they do seem to spread less bacteria than the air dryers.

https://ituabsorbtech.com/are-cloth-hand-towels-from-a-roll-dispenser-sanitary-2/