This scheme, introduced somewhere around Debian 5 "lenny", used udev to identify interfaces by MAC address and assign a fixed interface number to any interface it recognized (writing the rules to /etc/udev/rules.d/70-persistent-net.rules). This could have annoying side-effects (e.g. if you were replacing a machine's sole NIC, you'd also have to take special care to ensure it took over as network interface number 0) but these were minor and predictable.
Since Debian 9 "stretch", newly installed machines no longer start with an /etc/udev/rules.d/70-persistent-net.rules file, though such files are maintained if they still exist (with new lines added for newly installed network hardware). Debian 10 "buster" additionally lacks the /lib/udev/rules.d/75-persistent-net-generator.rules file that appends to it, though legacy 70-persistent-net.rules files are still honored. This support is expected to be removed from Debian 11 "bullseye" at some time before it is released.