Windows is a general applications OS, targeted largely at businesses. It has a very wide range of applications, many of which can be downloaded and run for free. It is notorious for the number of security holes it has, and has amazingly bad tech support.
MacOS is the operating system for Apple computers. It has a highly polished user interface, takes very little effort to use, and has decent tech support. Unfortunately, it isn't as popular as Windows, so you won't find the bredth of applications available for it. Also, if you want to do something cool, special and different, then you're hozed because the OS is designed around people who don't want to customize. MacOS really only runs on Apple computers, and the whole package tends to be more expensive than the Windows equivalent for the same power, although proponents aruge that the maintenance effort in Windows makes up for it.
Unix is a family of operating systems designed to run in a mainframe environment. There have been some efforts to make Unix work on PC's, but for the most part it remains the domain of large business systems. It has numerous user interfaces which tend to range from user hostile to badly outdated, but it works very, very effectively for server applications.
Linux is the most popular attempt to create a Unix-like operating system for personal computers. Until recently, Linux also had all of the limitations of Unix, with the sole benefit that you could run it on an Intel based PC. This one benefit has created an environment where pretty much anybody can write software for it, and they have. There's an amazing plethora of applications available for Linux. Unfortunately, they have traditionally been difficult to install, and not written by someone who had the user interface in mind. On the good side, both the operating system and most of the applications for it are entirely free.
Ubuntu has improved significantly on the "difficult to use" factor of Linux systems, but that is a story for another question.
The primary unique characteristic of mainframes is that they are multi-component systems, and each component tended to have its own processor. This differs from a desktop system because in that environment a single processor does all the thinking for most of the rest of the parts. This differentiation has been blurred recently, as desktop peripherals like video cards and storage devices have increased their intelligence in an effort to speed up their functionality and take load off of the main processor.