Abstract Art is the decending from realism in Art. After the invention of the photograph, allowing artists to explore new meanings in art rather then trying to replicate the world they lived in. The photograph, and later, the film,for the first time gave artists a way to pause and examine thier subjects for a much longer time. The artist started to experiment and added more creative freedom to what he portrayed on canvase.
Cubism, a type of abstraction, started to arrange subjects into geometric forms. They started to play with twisting perspectives and even mimicing forms moving in time. "Nude decending a Staircase No.2", by Marcus Duchamp, shows the movement of this decent down the staircase. Through the use of bold lines and emphises on the action, it gets ride of any figure repsentation. Unless you knew it was a person going down the stairs, you might think it was 'non-repsentational'.
Non-repersantional is art that has absolutely no connection to anything known in the real world.
An example of non-repersantional Abstract Art is Kazmir Malevich's Black Square, painted in 1915. It is simply a black square and represents no object in nature, but was still very popular and still renowned today.