There are four editions of Windows this time around: Windows RT, Windows 8, Windows 8 Pro and Windows 8 Enterprise.
Windows RT is designed for ARM CPUs, at the moment tablets only. It will run the new Modern UI apps, but will not run Desktop programs from previous versions of Windows.
Windows 8 is the 'standard' version for x86 and x86-64 (32-bit and 64-bit) CPUs, currently used on tablets, laptops and desktops, to replace Home and Home Premium. It will run both Modern UI apps and traditional Desktop programs. Most programs that run on Windows 7 will work here.
Windows 8 Pro is the 'premium' edition for x86 and x86-64 (32-bit and 64-bit) CPUs, currently used on tablets, laptops and desktops, to replace Professional and Ultimate. It has a couple extra features on top of Windows 8 (standard).
Windows 8 Enterprise is the business/volume licence edition, to replace Enterprise. As a home user, don't worry about this. It is similar to Pro, but missing media center. One notable feature is Windows-To-Go, which lets you boot off a flash drive.
Microsoft has a feature comparison of the different versions. Wikipedia goes into more detail.