The Modernist era emerged in the late19th Century with the early movements of Romanticism, Realism and Impressionism.

Modernism resulted from the want to experiment beyond what was deemed “traditional” and the need for self-expression. The unique "feature" about this era is that modern artists did not subscribe to a single style, but instead constantly pushed the boundaries of what "art" meant.

These artists began to challenge and reject the classical norms. They no longer wanted to follow the composition, colour, and subject matter, for example, of a piece of art from the Renaissance period (the era before the Modernist era) and instead sought to reinvent how art should look and feel.

Artists of the Impressionist movement, for instance, defied the usual conventions of painting in a studio, but instead, took their canvases out into the open, using the environment to inspire their work. To give an example, one artist of the era, Paul Cézanne borrowed natural geometrical constructions and injected this into his art pieces to simplify his works.

An example of a piece of work by Paul Cézanne that used natural geometrical constructions
Photo credit: Robert Genn

Events and issues happening in the real world also contributed towards the evolution of modern art. Early 20th Century happenings, such as The Russian Revolution and World War I, for instance, prompted future movements such as Cubism and Surrealism.

The Modern Art era lasted till the mid 20th Century with movements such as Pop Art and Neo-Dadaism.

Source:
http://arthistory.about.com/od/modernart/f/what_is.-Eoj.htm
http://www.arthistory.net/artists/paulcezanne/paulcezanne1.html