What is the name of the automatic backup feature introduced in Mac OS X Leopard?

The automatic backup feature introduced in Mac OS X Leopard is Time Machine.

Apple introduced Time Machine with Mac OS X 10.5 Leopard, released in October 2007. It was designed to make routine backups simple: users could connect an external drive, enable the feature, and let macOS preserve versions of files automatically. Its distinctive interface let people browse backward through earlier states of their files and recover documents that had been changed or deleted.

Time Machine is more than a basic file-copy utility. It can back up user files, applications, system data, and settings, and Migration Assistant can use a Time Machine backup when moving to a new Mac or restoring a damaged installation. It supports local disks and, in various macOS versions, network backup destinations.

A common mix-up is AirPort Time Capsule, which was Apple hardware that could store Time Machine backups; it was not the backup feature itself. Carbon Copy Cloner and Backblaze are third-party backup products. Much later, macOS Big Sur revamped Time Machine to use APFS more extensively, but that did not change its original Leopard-era name or origin.