To run ArcGIS on a Mac, the Mac must be set up to run Windows. There are severals ways to do this, but they require one of two installation options.
Option One: Create a dual-boot setup on your Mac, which allows you to boot into either Mac OS or Windows OS. The typical method for this is to use the free software BootCamp.
Using BootCamp: http://www.apple.com/support/bootcamp/
Option Two: Create a virtual machine on your Mac, which allows you to run an installation of Windows OS in parallel with your existing Mac OS, and to switch from one to the other without booting into either one separately. Typical choices for the virtualization option are the licensed software Parallels or VMware.
In order to achieve this there are some things that you are going to need to do:
1) You are going to need to partition the hard drive on your Mac:
2) You're going to need to install a virtual machine or Bootcamp on that partition
3) You're going to need to get yourself a copy of windows to install on that machine
4) Finally you will need a copy of ArcGIS: