i386 was the first x86 32 bit processor. What this means is that it'll run on practically any x86 CPU made within the last 22 years, but seeing that the architecture was designed so long ago, it's reasonable to expect that any operating system compiled for it isn't going to be running at optimal speed on today's latest and greatest processors.
i686 on the other hand is a much more modern architecture. It includes practically every processor that's Pentium II or better. x86_64 is a 64 bit extension to the x86 architecture. x86_64 processors can still run 32 bit operating systems (e.g. i386) if you so choose, but they're also capable of running 64 bit operating systems.
PowerPC (PPC) is the processor type that Macs used to use, but within the last few years Macs have also transitioned over to x86. Nowadays, PowerPC's main use is seen in modern game consoles.
So, to answer your question... if you have a 64 bit processor, you should get either an x86_64 or i686 optimized distro. If not, you should just get i686 (assuming of course that your computer isn't older than 10 years).