x86-64 is a 64 bit extension to the Intel x86 architecture
x86-64 is a 64 bit instruction set, backwards compatible with the 16 and 32 bit architectures originating from the Intel 8086 processor. It is sometimes known as amd64 (common in GNU/Linux) or x64 (usually only seen in Windows).
The specification was created by AMD, and has been implemented by AMD, Intel, VIA, and others.
See the x86 tag for programming and optimising guides and other resources.