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What is the different between i386 i486 i586 i686 architecture for software?

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1. They're instruction sets between different cpus. There is the original Intel i386 cpu. i486 came after. i586 is the first pentium, no mmx. i686 the latter set and is typically considered the generic default for 32 bit; pentiumpro cpu and up would qualify for this.
2. i386 is Intel's first architecture with a 32-bit virtual addressing mode, which is essential for all modern operating systems. i486 is pretty similar, except faster. And some added useful instructions. Most have a built-in FPU. i586 is the first architecture virtually guaranteed to have a FPU, and might also have MMX. Intel's 586 processors are known as Pentium. Also has some additional useful instructions. i686 is the generic name for all 32-bit AMD Athlons and all 32-bit Intel processors since the Pentium Pro and Pentium II. Starting with the 686, the instruction set and the architecture are decoupled, so there is less need to change the instruction set for new processors. Indeed, the instruction set wasn't changed until AMD's Opteron and Athlon 64 (adopted by Intel Pentium D), which is why that architecture is often known as amd64 instead of ia-32e or em64t or whatever awkward name Intel has for it.