Apple have a surprising amount of open-source software. The OS that MacOS and iOS are built on top of (Darwin) is open-source, as is its kernel (XNU). The engine used by Safari (Webkit, forked from KDE's KHTML) is open-source too.
It's not really traditional open-source, though. It does use an OSS license, but they don't really accept public contributions, nor do they track bugs publicly or have a public roadmap.