I see that Oracle 11g or 12c doesn't have the download files for OS X. However, there is a version of the SQL Developer available for OS X. What's the point of the SQL Developer when you don't have a database?
How do I install the Oracle database (preferable 12c or 11g Express Edition) on OS X?
You can't install the database server software directly on OS X1. Oracle made a decision some time ago not so support it any more, presumably because it wasn't used enough to justify the costs involved. I seem to recall its demise roughly coincided with Apple dropping their Xserve line, but I may have imagined that.
A client like SQL Developer is a very different proposition from a support perspective. SQL Developer is a Java application, and requires a JVM/JDK to be installed. Java's write-once-run-anywhere may not be entirely true, but it's still likely to be rather less work to support a relatively small Java application than a natively-compiled beast like an full RDBMS. They obviously have to do some work to have a .app bundle and there are some application difference from the Windows version, but they don't have to worry about different architecture, system libraries, etc. as that's the JVM's problem.
You can use SQL Developer on a Mac to connect to a database running on Windows or Unix/Linux etc., so it still has a place; the fact you can't have a local server running on the same hardware isn't really relevant for most people. It just allows developers to use a Mac instead of forcing them on to a Windows or Linux PC.
If you only have access to a Mac then the simplest route is still as noted before, to install VirtualBox and one of the pre-built VM images Oracle provides.
You can also install Windows or Linux on Bootcamp or in your own VM in Virtualbox, Parallels or VMWare; and then install Oracle natively. Using a pre-built image saves you needing to learn how to install the database server software, and also makes it easier to go back - if you really mess something up you can trash it and start again fairly simply.
If you're worried about performance or power use I'd suggest you start with a VM and see how you get on; you can always add Bootcamp later and even move the data across if you want to go down that route.
1 You could try to hack something together of course; it's been done before with 10g but I haven't seen anyone trying it recently so it may not be as easy on Yosemite and 11g/12c.