Revit only runs on Windows. However, you can run Revit on your Mac by installing Windows on your Mac. There are two ways to do this: Boot Camp and via a Virtual Machine (VM).
Boot Camp is very straight forward. It's essentially "dual booting" your Mac. Once Windows is installed in the Boot Camp partition, you'll have the choice at startup to either boot into OS X or boot into Boot Camp (Windows). Once in Boot Camp, you're for all practical purposes using a generic Windows PC just like any Dell, HP, etc. All the CPU, GPU and RAM is dedicated to Windows. You can install any Windows software you want, and it will run pretty much exactly like it would on a PC with the same hardware specs – same speed and everything.
There's obviously one major drawback: you won't be able to access OS X from Boot Camp. None of the OS X apps will be available. While in Boot Camp, you're stuck in a Windows world. However, it will by far offer the best performance, so if you're going to spend a lot of time working in Revit, especially larger projects, or you need to let a rendering cook overnight, Boot Camp is probably your best bet.
Virtual Machine (VM)
Virtual machine software (also often referred to as "virtualizaton") "creates" a generic PC hosted in OS X. The software borrows RAM and CPU resources from OS X to power the VM. Using the VM software, you install Windows on this "virtual" PC - no partitioning of your storage drive is needed - the VM is stored as a file that is accessed by the VM software. You then can boot into Windows from within OS X, and have both operating systems running at the same time. This virtual PC really thinks it's a PC – you can install almost any Windows software on it, including Revit, and it will run. Unfortunately this nifty trick doesn't come without a significant loss in Revit performance.
Two things happen:
First, the VM is borrowing hardware resources from OS X to run Windows – so that means OS X has less resources for itself, which may slow down or limit your OS X apps. On the other side, the VM only has access to the hardware resources you allow it to have. So if you have a 2 core CPU, OS X gets to use one, and the VM get to use one. If you have 8 GB of RAM, you might give 4 GB to the Windows VM (which isn't that much for Windows and Revit!) and keep 4 GB for OS X (or whatever combination you want - however, while the latest versions of OS X can work with as little as 2 - 4GB for itself, it can be a little tight).
Second, because the VM is running inside of OS X, much of the PC hardware is being virtualized – it's kind of like everything that happens in the VM on a hardware level needs to be translated back into something that OS X can understand. This hardware translation takes a toll on performance, particularly with the GPU, resulting in relatively slow graphic performance. Since the VM software can't use specific drivers provided by hardware manufacturers, it provides all of its own virtual generic drivers which may not be fully optimized and don't have the necessary direct access to the hardware layer to be as fast as in Boot Camp.
With that said, Revit can run fairly well (though not very fast) in a VM, provided your Mac has enough CPU speed and RAM. It's certainly more convenient to still have access to all your OS X apps and data at the same time. Whether you'll be satisfied with performance depends mostly on your Mac's hardware specs and your expectations. If you already have a Mac, it's easy enough to try out yourself. If you're planning on buying a Mac for this intended purpose, I'd strongly recommend seeking out a friend or associate with a similar Mac to try it out (also Apple also has a good return policy if you purchase directly from them).
My personal experience: I have a Mac Pro (late 2013) at home: Xeon E5-1620 v2 3.7 GHz (3.9 GHz with Turbo Boost); 12GB RAM; AMD FirePro D300, and I find Revit 2015 painfully sluggish compared to when in Boot Camp or my PC at work (i7-4770K 3.6 GHz (4 GHz with Turbo Boost); 16 GB RAM; Nvidia GTX760Ti). However, YMMV.
VM Software Options
There are three major VM options: Parallels Desktop for Mac, VMware Fusion, and Oracle VirtualBox.
Parallels Desktop was first on the scene for Intel-based Macs, and is very popular. It's known for being a very fast performer, though has been criticized for being a bit more buggy at times than VMware Fusion. The latest version of Parallels supports DX10 (DX11 is required for Revit's full graphic feature set, but none of the VM's support DX11 - frankly, I'm not sure how much of a difference it would make if they did), and retina displays (see more about retina below).
VMware Fusion was released shortly after Parallels Desktop, but is from software vendor VMware, which is has a very long history with virtualization software on the PC side of things. Fusion is known for being very stable, but has been criticized for often being slightly slower than Parallels. The latest version of Fusion 7 is still stuck on DX9, so the graphic features may be even more limited. It does have support for retina displays (see more about retina below).
Both Parallels and Fusion cost about $80 US, plus you'll need to purchase a genuine copy of Windows to install (note that if you have an old copy of Windows laying around from a Dell, HP, etc., OEM versions of Windows often will refuse to install or activate on any PC other than the original one it came from). Both are offered as limited-time trial versions, and I'd recommend taking both for a spin and seeing which one works best for you.
VirtualBox is free (though you still need a copy of Windows) and open-source software. VirtualBox is great software for being free software, but it's much more difficult to use and not nearly as fast, slick or feature complete as Parallels and Fusion. Feel free to give it a shot – it might be perfect for occasional use, but if you're going to be doing a lot of Revit work in a VM, I'd recommend getting Parallels.
VM Performance Tip: Gordon Price suggests this for improved performance: Within your Windows VM, find the AdskHardwareCertificationReport.xml file (usually in C:\Program Files\Autodesk\Revit 20xx). Rename it something like AdskHardwareCertificationReport.OTTB. This file is used to check whether the hardware is "certified" for use with Revit, and if it isn't, it may prevents hardware performance enhancements that could otherwise be taken advantage of. Renaming it will prevent the hardware check, and appears to lead to better performance in many cases.
Macs with Retina Displays
Retina displays offer a super high resolution display that looks amazing in OS X. The way OS X works with a retina display is to effectively double the size of every element on the screen, but since the retina display resolution is twice a normal display in each direction, everything looks the same size as a normal display, only twice as sharp. Windows, and Windows applications like Revit, were never really designed with this concept in mind. This results in a couple of issues - icons and text can get very small or the application's user interface can get way out of whack. There are a few ways to handle this, but they may not be completely satisfactory to you.
Retina/HiDPI/4K/5K Display using Boot Camp
See the section "4K/5K & HiDPI & Retina Displays" in the Hardware: Video Graphics Cards post if you're using a Retina or similar HiDPI display.
Retina Display Using a VM
Working with Windows on a retina display using a VM is very similar to the experience of Boot Camp. Parallels and Fusion have settings in the VM's configuration, which effectively change the DPI resolution to 200%. This will likely break Revit unfortunately. You'll probably want to use one of the techniques suggested above for Boot Camp.
Definitely check out these support articles:
Parallels Mac support article on troubleshooting retina display issues with Windows.
VMWare Fusion support article on troubleshooting retina display issues with Windows.
If you're getting a Mac intending to use Revit extensively or full-time on it, spec the fastest CPU available, make it a quad core if available, and 8 GB of RAM minimum if you'll mostly be using Boot Camp, and 12 GB of RAM minimum if you'll be using a VM. Keep in mind that many of the most recent Macs make future RAM upgrades very difficult or even impossible, so you may need to anticipate your future needs - in most cases, I'd recommend 16 GB from the start. Parallels or Fusion - has generally been a toss-up - I've used both extensively over the years, but now I stick with Parallels because of its faster performance.
I've been a computer enthusiast for over twenty years. I know a lot, but I don't know everything. Drop me a PM with suggestions, or if you spot any errors, or think something needs further clarification, or feel free to take it up with me in the forums. And *post* those questions, requests for advice, and solutions! (and generally speaking, please don't PM me with support questions - the forums are here for everyone to share their questions and answers - you might think your question is unique to you, but there are likely others who can also benefit from the discussion)