macOS (or OS X, or Mac OS X, as it has been variously called) has had 13 major versions. Each brings with it new capabilities, but each also drops some older ones as well. Here is a non-comprehensive list of some of the things I might use an old version of macOS for:
10.0 Cheetah, 10.1 Puma, 10.2 Jaguar, 10.3 Panther: These are so old I have no occasion to run them.
10.4 Tiger: Last version to include Classic environment, which enables running MacOS 9 software on Macs with Motorola PowerPC CPU’s.
10.5 Leopard: Last version to support to support printing to AppleTalk printers on a network. Last version that runs on Macs with Motorola PowerPC CPU’s.
10.6 Snow Leopard: Last version to include Rosetta, which enables running software written for Motorola PowerPC CPU’s. Last version to support iSync, which synchronizes address book information via USB or Bluetooth with older mobile phones. Last version that runs on Macs with 32-bit CPU.
10.7 Lion: Last version that runs on Macs with 32-bit EFI ROM.
10.8 Mountain Lion: Last version to support Sync Services, which synchronizes address book and calendar information between the Mac’s Calendar and Contacts applications and other Mac Apps (such as Entourage and Outlook 2011). Last version to support fully manual configuration of Apple Mail.
10.9 Mavericks: Last version that performs acceptably on hard drives (as opposed to solid state drives). Last version to support download headers only in Apple Mail, rather than entire messages.
10.10 Yosemite: Last version to support “unenhanced” iCloud notes syncing used by older iOS versions.
10.11 El Capitan: Last version to support Apple Java 6. Last version to support somewhat manual configuration of Apple Mail settings. Last version that runs on Macs with older wireless hardware (Broadcom 4300 series).
h/t to the Wikipedia articles on the various individual versions of macOS for reference and memory-joggers.