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The term x86 is shorthand for 80x86, which was used to refer to any member of the family 8086 (and also, incidently, 8088), 80186, 80286, etc. Things have since gotten a bit muddled by the fact that while an 80386 had a mode that was compatible with the old architecture, it also introduced some fundamentally new ways of doing things which were shared by the 80486 as well as "named" processors like the Pentium, Pentium Pro, etc., and thus it is sometimes ambiguous whether the name "x86" is used in reference to the architecture that started with the 8086, or the one which had its debut with the 80386.

x is meant as wildcard, so this represents all CPUs able to run 8086 compatible code.

In modern usage it also means software which only uses the 32-bit architecture of the earlier 80x86 processors, to distinguish it from 64-bit applications.

Microsoft uses it that way on 64-bit versions of Windows, which have two separate directories called "Program Files" and "Program Files (x86)."

The 32-bit applications will run on 64-bit hardware, but the OS needs to provide the appropriate 32 or 64 bit interface at run-time.

Intel products were numbered. For example, their first microprocessor was the 4-bit Intel 4004, which was coupled with the 4001 ROM, 4002 RAM, and 4003 shift register. The start denoted the series, and the last digit denoted the specific part.

Later, the intel 8008 came along, which was an 8-bit microprocessor. This was succeeded by the 8080, which was then replaced by the 8085, which was then replaced by the 8086.

After the 8086, processors started taking on the format of 80x86, with x being a number such as 80186, 80286, 80386, etc. They were backwards compatible with one-another, and modern computers still boot into 16-bit-mode. As Intel continued rolling out processors, they began to be referred to as Intel 386 or Intel 486 rather than Intel 80386. This is how the terms 'i386' and 'i586' came into play. As they were based on the same architecture, they were called Intel x86, where x refers to a number. They also came with coprocessors that had a last number of '7', such as 80387, and as such we also have x87.

It just means any processor compatible with same architecture.
So it includes 8088, 8086, 80186, 80286, 80386, 80486, Pentium, etc..

The name "x86" was never 'given' or 'desiged' this way. If I remember correctly, it more or less evolved as a convenient abbriviation for a whole range of compatible processors.

Back in the day when PC's became populair, it was important that your PC was "IBM Compatible". This meant, among other things, your PC must have an Intel 8086 or an 8088. Later, when Intel released more powerfull processors such as the (rare) 80186 or (popular) 80286, it was still important that your PC was just "MS-Dos" or "IBM Compatible". The 80286 was just a faster processor. It had a protected mode feature, but little software actually used or even required that.

The next step was the 80386. This was an improvement over the 80286 because it had a mode that provided full backward compatibility with 8086 programs. Operating systems such as OS/2, DesqView and MS-Windows used this mode to provide backward compatibility whith existing software. Other operating systems such as Linux and *BSD's designed for PC hardware also depended on some new features of the 80386 without acutally providing direct compatibilitiy with existing MS-DOS software. All these systems required a 80386 processor.

Then came the 80486. An even faster and more powerfull processor but mainly backward compatible with the '386. So if you bought a '486 you could still run software designed for the '386. The package would say 'needs a 386 or better' or 'needs 386 or 486'

Along came the 80586 or Pentium. And then the Pentium Pro, also known as 80686...

By this time software developers got tired of listing all possible numbers and since most software was still written to be able to run on a '386, the whole list of numbers was abbriviated to just "x86". This later became synonymous with "32 bit", because the 80386 was a 32 bit processor and hence software that's written for 'x86' is 32-bit software.

Practically x86 is shortening for "80386 or 80486 running in 32-bit mode". It comes from 8086/186/286+ line but Win32 cannot run on CPU below 386. After 80486 the 80*86 scheme was changed to Pentium[N] and AMD [model].