A Happy Mac is the normal bootup icon of an Apple Macintosh running older versions of the Mac OS. It was removed with the introduction of Mac OS X v10.2, which replaced it with a large grey Apple logo.
When you boot a Macintosh, it makes a startup chime and the screen turns gray. After a few seconds a Happy Mac icon will appear, followed by the splash screen of whatever version of the Mac OS you are running. The Happy Mac indicates booting has successfully begun, whereas a Sad Mac indicates a problem in the bootup sequence.
On early Macs that had no internal hard drive, the computer would boot up to a point where it would need to load the operating system from floppy disk. Until the user inserted the correct disk, the Mac would display a blinking disk icon. The blinking disk is still sometimes seen on hard drive-based systems when the disk is unbootable. The Happy Mac may appear briefly before the blinking disk icon.