Feynman considered a number of interesting ramifications of a general ability to manipulate matter on an atomic scale. He was particularly interested in the possibility of denser computer circuitry and microscopes that could see things much smaller than is possible with scanning electron microscopes. Researchers at IBM created today's atomic force microscopes, scanning tunneling microscopes, and other examples of probe microscopy and storage systems such as Millipede.
Feynman proposed that it could be possible to develop a general ability to manipulate things on an atomic scale with a top-down approach. Use ordinary machine shop tools to develop and operate a set of one-fourth-scale machine shop tools. Use these to develop one-sixteenth-scale machine tools, including miniaturized hands to operate them. Continue on until the tools are able to directly manipulate atoms. This will periodically require redesign of the tools, as different forces and effects come into play. The effect of gravity will diminish, the effects of surface tension and van der Waals attraction will increase.
He concluded his talk with challenges to build a tiny motor and to write the information from a book page on a surface 1/25,000 smaller in linear scale. He offered prizes of $1000 for each challenge. Unfortunately, his motor challenge was met by a meticulous craftsman using conventional tools— met the conditions, but did not advance the art.
Feynman's talk did not describe the full nanotech concept, though. It was K. Eric Drexler who envisioned self-replicating nanobots in Engines of Creation: The Coming Era of Nanotechnology.