"Nanochip" is a term referring either to a typical computer chip, which has feature sizes measured in nanometers, or some novel computer design based on "nanotechnology," another vaguely defined word. Basically, the word is vague enough that you can theoretically use it to refer to any modern computer chip.
More specifically, the term "Nanochip" is most often associated with Nanochip, Inc., a company attempting to use MEMS (micro-electro-mechanical systems) technology to create a high-density storage device that leapfrogs improvements in traditional storage methods, which are based on photolithography. Nanochip's technology uses arrays of tiny atomic force probe tips to electrically write to a storage medium. The probe tips are only 25 nm across, and can edit areas of the storage media with a precision of 10 nanometers or less. According to the company, this could enable microchips with 100 GB storage capacity by 2009, and terabytes (TB) further down the line.
Nanochip, Inc. is backed by various VC firms and larger chip companies including Intel. Its array probe technology is reminiscent of IBM's Millipede, a defunct project that used a similar approach. Millipede was apparently abandoned sometime around 2006, for unknown reasons. Meanwhile, Nanochip has been working on its technology since 1996, but only began receiving media coverage around 2007. It remains to be seen whether Nanochip's technology will see the light of day or whether it will fail like Millipede.
Sometimes, the word "nanochip" is also used to refer to conventional computer chips that integrate carbon nanowires into their structure. Carbon nanowires are highly conductive and chips that use them cannot be manufactured exclusively using traditional photolithography — they must go through two manufacturing stages, one for the conventional chip and one to add on the nanowires.
Nanowires are useful for computing because of their very small size and high conductivity. Sometime between 2015 and 2025, it seems feasible that computers will be built almost exclusively out of carbon nanowires, but for now, we're in a transitional period between chips manufactured using photolithography and chips made with more advanced methods.