I have BOX MS Office 2010 and run it on my Windows machine. Can I install it/migrate licence to OS X?
No, you cannot migrate your license from Office for Windows 2010 to Office:Mac 2011.  You will need to purchase a new license for Office:Mac.  

You could run Office for Windows on your Mac.  If you have a license for Windows, you could install Windows either using Boot Camp or a virtualization application like VMware Fusion or Parallels.  After you have installed Windows on your Mac, you can then install your existing copy of Office for Windows.