Can't upload to my Nano after updating to Arduino AVR Boards 1.6.21

Arduino recently changed the bootloader they ship on their official Nano boards. This required a change in the hardware definition for the Nano, which was the sole reason for the Arduino AVR Boards 1.6.21 release.

The new Nano hardware definition is not backwards compatible with Nanos that use the previous ATmegaBOOT bootloader. For this reason a new menu option was added: Tools > Processor > ATmega328P (Old Bootloader). If you select that option the uploads to your Nanos will work again.