It is an implementation of the Windows APIs for Linux.
That means you can run Windows apps just like normal apps. They appear in their own windows, they integrate with the system tray, can read your linux home directory etc. You don't need a copy of windows to do any of this.
However Wine is in alpha, and has been for a long time. Windows is a moving target. Lately they have been doing well, and you can run MS Office, Internet Explorer and so on. They don't work perfectly, but in general they do work. I use IE all the time on Linux (for web development).
Don't bother with the builds from WineHQ. They are not easy enough to set up. If you actually need Wine, as opposed to just wanting to play with it, buy CrossOver from CodeWeavers Inc. It's definately worth it.