artists depiction of scary nanobot standing with 6 long sharp pointed legs and a single camera for an eye

The following is a detailed definition of a nanobot from Wikipedia, but I can tell you a whole lot quicker. It is a really, really small robot.

Actually, from what I've read in the links I've collected below, they should not even be called nanobots, maybe microbots or biobots would be a better name.

Nanobots do not exist yet, but when they do, futurists predict possible uses for nanorobots will include molecular manufacturing (nanofactories) and medical nanobots that steer autonomously through your blood stream making repairs and guarding against infection.

The bad side of nanobots will be their obvious suitability for spying and the possibility, however unlikely, of a nanobot takeover, aka grey goo.

Nanorobotics is the technology of creating machines or robots at or close to the microscopic scale of a nanometer (10−9 meters). More specifically, nanorobotics refers to the still largely hypothetical nanotechnology engineering discipline of designing and building nanorobots, devices ranging in size from 0.1-10 micrometers and constructed of nanoscale or molecular components.

As of 2010 nobody has yet built artificial non-biological nanorobots: they remain a hypothetical concept. The names nanobots, nanoids, nanites or nanomites have also been used to describe these hypothetical devices.

Grey Goo

Grey goo (alternatively spelled gray goo) is a hypothetical end-of-the-world scenario involving molecular nanotechnology in which out-of-control self-replicating robots consume all matter on Earth while building more of themselves, a scenario known as ecophagy ("eating the environment").

Self-replicating machines of the macroscopic variety were originally described by mathematician John von Neumann, and are sometimes referred to as von Neumann machines. The term grey goo was coined by nanotechnology pioneer Eric Drexler in his 1986 book Engines of Creation, stating that "we cannot afford certain types of accidents." In 2004 he stated "I wish I had never used the term 'grey goo'."


Size Matters

diagram showing size differerence starting at DNA

This illustration from gives visual examples of the size and the scale of nanotechnology, showing us just how small nanotechnology actually is.

A nanometer is one-billionth of a meter. In comparison, a human hair is about 100,000 nanometers in diameter.

All dimensions are approximate. Nanoparticle is courtesy of the National Center for Electron Microscopy, Lawrence Berkeley Lab, US Department of Energy.

Another illustration of size comparison can be found here:
"The scale of things"