Nanotechnology is literally technology on the nanometer scale. A nanometer is one billionth of a meter in length. In other words, this is engineering technology on the molecular level. If we can design and create technology on this scale we can literally control and build matter at the molecular level. The applications for this include medical technologies and materials science. With materials science, we could use nanotechnology to build new chemicals and materials with specifically designed properties to be used for things like solar energy production or faster and more efficient microchips. With medical technologies, we could engineer new methods of fighting diseases programmed at the molecular level so as to avoid toxicity issues that are inherent to broader based treatments (like chemotherapy or radiation for fighting cancer). Potential risks would be a loss of control or the use of the technology as a weapon.
Nanotechnology is basically technology specifically small machines and robots on a molecular scale. One of the most highly touted uses is curing diseases. Imagine that instead of just white blood cells fighting a virus in your body you could be injected with small machines that assist in the fight, or small robots that will destroy a tumor etc. The risks are the same as with any medicine. There is always the possiblity of side affects or for them to be weaponized and programmed to destroy healthy tissue. The benefits however are vast including an end to most cancers and many viruses.