A backless dress is one cut so low at the back that the wearer's back is completely exposed. It may even reveal rear cleavage. It may also have a halterneck for extra support. The idea is to keep most of your front covered to look classy, while revealing enough skin to look daring and sexy.
Backless dresses were mainstream fashion in 1930s evening gowns, and have made periodic reappearances since (often with the sides of the back covered, unlike the illustration).