x86 is an Intel CPU architecture that originated with the 16-bit 8086 processor in 1978. Today, the term "x86" is used generally to refer to any 32-bit processor compatible with the x86 instruction set.
In its 40 years of existence, the x86 architecture has added many new features while remaining almost entirely backward-compatible, which is a remarkable achievement.
Modern 64-bit processors are generally referred to as x86_64, although they may also be referred to as amd64. The amd64 label is in reference to AMD being at the forefront of 64-bit processing technology in the early 2000s. Regardless of the label, these processors (and the software compiled for them) are based upon, and compatible with, Intel's x86 architecture.