The x86 architecture is two architectures defined as one. It is the combination of these two architectures, that through compatibility, create the most dominant computer architecture on the planet.
First is the central processing unit (CPU) itself. Fundamentally the x86 CPU is a variable instruction length Complex Instruction Set CPU (CISC) with emphasis on backward compatibility. Created in the late 70's, and improved several times over the succeeding decades. Each new generation, maintaining compatibility with the previous generations, has allowed the x86 CPU to continue to run previous generations of software on current generation hardware. This makes for a compelling argument to use this architecture.
The second architecture is the complete computer architecture. The PC was conceived in the early 80's and it too has been improved several times over its now. Compatibility has always been the mantra. In those early years, designers that failed to recognize the power of compatibility saw their computers fail in the marketplace. Eventually, most stopped trying to make it better by making it different. Designers have learned to make it better while maintaining the system architecture compatibility.
Although newer architectures such as PowerPC have challenged the x86 as an alternative for many niches, none have supplanted the x86 architecture's dominance in the world of computing.