...for playing games?
Currently, the Mac OS X version of BYOND (like the Linux version) is text-only. Most BYOND games are graphical, so you won't be able to play them using the Mac OS X version.
If you want to play graphical BYOND games on a Mac, what you could do is run the Windows version of BYOND under Mac OS X by using an "emulator". If you have an Intel Mac, you can use Parallels along with a genuine copy of Windows (you'll have to buy them both) for this purpose. VMware Fusion and VirtualBox (free) are other options.
There are other free programs out there such as qemu and bochs, but they don't tend to work very well yet - though they are improving.
...for hosting or making games?
The Mac OS X version of BYOND can compile and host games without any problems, provided you don't mind working with the command line. See the included documentation.
If you're not comfortable with the command line (or don't know what the command line is), then we recommend using the graphical Windows versions of BYOND's game creation and hosting tools via an emulator, as described above.