Classic Mac OS
The first Macintoshes used the Motorola 68000 (68k) processor architecture. Their operating system was Mac OS. By System 7, Mac OS provided color graphics and sound. Because the system used cooperative multitasking, games could monopolise the hardware or crash the operating system. The normal way to obtain games was to copy them from 3.5-inch floppy or CD using the Macintosh Finder or an installer program. With larger games, one would install a program from CD, and then leave the CD and its data inserted while playing the game.
When Apple switched to using the PowerPC processor architecture, Mac OS provided a transparent 68k emulator so that old games could run on newer PowerPC computers.
Annoyingly, many games set the screen to only 256 colors (8-bit color depth); switching to the Finder or another program while playing them game would sometimes reveal blinking colors and wrong colors. Mac OS 8 introduced antialiased fonts, which would be disabled when there were only 256 colors.
The iMac became the first of the "New World" computers; Macintoshes started having ATI or nVidia cards with accelerated 3D graphics. Some games used Apple's QuickDraw 3D technology, but by Mac OS 9, OpenGL was dominant.
Mac OS X
Mac OS X combined Mac OS with NextStep. Old Mac games would only run in the Classic emulator unless they were ported. (If they were ported to "Carbon", they sometimes worked on Mac OS 8, 9, and X without an emulator.) Especially for full screen games, many games failed to work in the Classic emulator. This required rebooting the computer to Mac OS 9.
Mac OS X can run some Unix games. It is possible to play Unix games that use X11, but this requires installing X11, then rebuilding the game from its source code (as you would for any Unix variant) or obtaining the game from fink. Those games are found on the Unix page.