Why doesn't this linux thing I downloaded work? And why is I686 a problem?

...Because you downloaded the wrong architecture ya doofus.

If you are exploring different OS distros and download an iso and then burn a disk and then go to run it and it doesn't work because of an architecture issue? You've just wasted your time downloading an architecture flavor of no use to yourself and probably frustrated yourself along the way. But fret not. Below is some education to circumvent the feeling of helplessness you're experiencing.

A Brief Explanation of CPU Naming Schemes:

The X86 processors started with the Intel 8086 processor way back in 1978. They were incrementally improved (80186, 80286) and then Intel released the Intel 386 (i386) in 1980. That was then followed by he 486 (i486), the Pentium (i586), and the Pentium Pro/2/3/4 and Celeron (i686). At the same time, rival AMD released their Athlon/Duron/T-bird (also i686).

Since all these processors were based on the same architecture (basically they read/wrote 1's and 0's in the same way), and their names all contained "86", the whole family was collectively called "X86". All the X86 processors including and after the 386 are 32-bit.

The difference between a Pentium/Celeron and an Athlon/Duron or Athlon/Sempron is that Pentium and Athlon are the top-performing, more expensive models whereas the Celeron/Duron/Sempron are cheaper, less powerful chips. They are not a different architecture.

Since 2000, the trend has been to move toward 64-bit processors, and several different architectures popped up. DEC's Alpha and Motorola's PPC chips have been 64-bit for a while, but Intel's Itanium and Xeon and AMD's Athlon64 are the new kids on the block.

The difference between the Itanium (IA64) and PowerPC (PPC) versus the Athlon64 is that the Itanium and PPC have completely different architectures (they speak different 1 and 0 languages), whereas the Athlon64 speaks the same language as the 32-bit X86 processors, but adds 64-bit memory registers. Therefore the name of the Athlon64 in generic terms is "X86_64".

Intel, not to be outdone, has since redesigned its 64-bit Xeon processors to use the same kind of architecture as the Athlon64, calling it "Intel Extended Memory 64 Technology" (EM64T). Basically they couldn't say they copied AMD without being laughed at in irony (since AMD got its start by simply copying Intel's chips). Both the AMD64 and the Intel EM64T processors are collectively called "X86_64".

The Intel Core processors come in two types. The original Core Duo processor is a 32-bit processor with two cores (i686). The Core 2 Duo is a 64-bit processor with two cores. The Core Duo (to the best of my knowledge) is a regular X86 processor, while the Core 2 Duo is an X86_64.

Certain models of the Pentium 4 processor (not just the Xeon) were shipped with "EM64T" technology. These processors (such as the Intel Pentium 4 521) are essentially the same as an AMD64 in their architecture, and are capable of running both 32-bit software and OSes as well as 64-bit. Software compiled for AMD64 should work on these processors.

In 2008, Intel developed a new brand name called i7, which despite its confusing name is NOT a new i786 architecture. Instead, it's just another set of X86_64 chips. For more information, look here.

Source

Learning is fun isn't it kids. Now you won't be wasting bandwidth downloading the wrong distro flavour.