i386 and i686 are identifiers that indicate what type of processor the system will run on. i386 means that the system was compiled for the Intel 80386 (a very old processor), and is upwards-compatible with all other x86 processors, including the latest i7s and Phenoms. i686 indicates that the system was compiled for the Intel Pentium Pro, and will thus run on that and all newer x86 processors (from the Pentium II to current processors), but will not run on an 80386, 80486, or the original Pentium.
If given a choice, you will generally want a distribution compiled for i686, as it will perform slightly better on newer processors than i386.