Imagine taking a sheet of graphite, a simple planar assembly of carbon atoms disposed in a honeycomb lattice, and rolling it up to form a cylinder. You would obtain a very long, yet very thin cylindrical object. It would have properties similar to those of graphite, be flexible but very hard to stretch. You could assemble these cylinders together in ropes, or nest several of them, with increasing diameters, like a russian doll…  

Rolling up a graphene sheet to form a nanotubes... from Odom et al, J. Phys. Chem. B104, 2794 (2000).

Since 1991, the dream of fabricating, manipulating, characterizing and modifying such cylindrical graphitic structures has become true. These objects were named carbon nanotubes and arose to one of the most fascinating materials that have been discovered in recent years.

A ball-and-stick model of a single-wall nanotube... and the real stuff: multiwall nanotubes as observed by electron microscopy

You want to know more? The primer is divided in five sections:

Nanotube basics

Nanotube production

Electronic properties

Field emission from nanotubes

Applications

Simply follow the links!