x86 is the generic name for Intel processors released after the original 8086 processor. These include the 286, 386, 486, and 586 processors. As you can see, the "x" in x86 stands for a range of possible numbers. Technically, x86 is short for 80x86 since the full names of the processors are actually 80286, 80386, 80486, and 80586. The "80" is typically truncated to avoid redundancy.
If a computer's technical specifications state that is based on the x86 architecture, that means it uses an Intel processor (not AMD or PowerPC). Since Intel's x86 processors are backwards compatible, newer x86 processors can run all the programs that older processors could run. However, older processors may not be able to run software that has been optimized for newer x86 processors.
While numbers provide a simple way to distinguish between processor types, they cannot be trademarked. For this reason, Intel's 586 processor is formally known as the Pentium processor. However, software developers still often refer to processors by their number. Of course, what else would you expect from computer nerds?