In a very broad sense, style is the way in which form and composition are combined to make a piece of art stand out.
The analysis of style is one of the primary areas of study for lovers of art and art historians because it allows them to identify the works of individual artists and to group works created in a similar style and manner. Some of the most common ways to distinguish different styles in arts have to do with time periods (period style), geographic locations (regional style), people belonging to particular groups (representational style) and more.
Realism, idealism, illusionism and abstraction are examples of representational styles.
Realism is also known as naturalism. Realists tried to represent the world around them in a visually accurate way.
Idealism describes works of art that idealize the objects that they deal with according to the prevailing values of a culture during a certain time period.
Illusionism is a style described by high attention to detail. Illusionists meticulously describe visual appearance of the objects to achieve an illusion of physical reality.
Abstraction, in its turn, departs from trying to describe the world accurately in a physical way and tries to capture the essence of the form, not necessarily its look.