There are many options for running Windows programs on the Mac. Boot Camp, for instance, is included with OS X for installing Windows on a separate partition. Parallels, VMware, and Sun offer virtualization software that let you run your Windows programs without logging out of OS X. And then there's Wine.
Wine is an Open Source application layer that runs within the Mac operating system rather than as a stand-alone, sandboxed operating system. The thing that all of these options, except Wine, have in common though is that they legally require you to actually run Windows and therefore own a Windows license. Wine, however, implements the Windows API allowing you to run Windows applications without actually running Windows.
David Baumgold has put together an excellent tutorial for setting up and using Wine on your Mac. The tutorial does a good job covering the pre-requisites, the actual installation, and then what to do with Wine once you have it installed. It should be noted that the installation of Wine is rather technical and should not be attempted by those unfamiliar with Terminal.app.
Once you get Wine up and running, you can install a myriad of different Windows applications from games to productivity apps (Office, anyone?). If you're curious about a particular program's compatibility with Wine, you can check out the AppDB for a list of applications and any issues present when running with Wine.
If you're interested in the technical benefits of Wine, you can also check out the excellent application Crossover, which is an easy-to-use port of Wine (pun intended) that makes it dead simple to get up and running with Wine.