You will find many differing definitions of what Modern Art or Modernism is in the scholarship of Art History. In a nutshell, Modern Art is "A term generally used to cover art of an avant-garde (progressive) nature from the beginning of the 20th century onwards." (from The Concise Oxford Dictionary of Art Terms, 2 ed.)
Mid-to-late 19th century works are included within Modern Art pedagogy, and you will most likely start here when learning about the history and development of the avant-garde. Hence, there is no precise "beginning" to the modern art period, and it is also up for debate when modernism "ends" and the contemporary period begins. What we do know is that the modern period saw radical changes in the way art was made, thought about, and taught. You will learn about all the "isms" associated with the period and applied to movements in painting, design, photography, architecture, theater, and crafts, including Expressionism, Pictorialism, Fauvism, Surrealism, Cubism, Constructivism, Dada, Bauhaus, etc. etc. etc!
[left] Raoul Hausmann, ABCD (self-portrait), a photomontage from 1923–24, [right] Market at Minho by Sonia Delaunay, 1915.
The Bauhaus, Dessau, Germany, designed by Walter Gropius (1925-26)