A 64k intro is a demo where the size of the executable file is limited to 64 kilobytes, or 65,536 bytes. At demo parties there is a category for this kind of demo, where the one that gives the best impression wins.
64k intros generally apply many techniques to be able to fit in the given size, usually including procedural generation, sound synthesis and executable compression.
The size of 64 kilobytes is a traditional limit which was inherited from the maximum size of a COM file.
A revolution happened when fr-08 was released in 2000.