There are many theories explaining this painting, but the following interpretation seems to be the closest to the artist’s philosophy. As you know, Malevich was the founder and the inspirator of the suprematism movement - the direction in art whose main idea was that art can be free from objective associativity (we are talking about material objects), and does not necessarily need to be figurative. In other words, Malevich and his followers believed shapes, colors, and composition themselves could be the means of communicating meanings. “Black Square” is the embodiment of this idea; its shape - the square, according to Malevich, is the basic suprematic shape - and its blackness (or the absence of color) symbolizes the beginning of non-objectivity, and the end of the traditional artistic “objective” way of thinking. “Black Square” is a dot, a period in the end of the long “sentence” of traditional art.