Contemporary is a dance form that grew and evolved with modern art movements. It has less strict form than ballet and exists in the ‘now’ with many personal expressions of form and possibility. It is an active and evolving form which involves whole body movement in space and time.
Contemporary has many different and idiosyncratic dimensions, reflecting the dance choreographer or performer. It is incorporated into the training and repertoire of many dance schools and companies throughout the world. It can be seen in the work of Sydney Dance Company and Australian Dance Theatre, amongst others, and is the training for many Australian independent dancers (independent of dance companies)
While there is no typical contemporary dance class, expect to work on the floor, standing and travelling. As in a ballet class, there is likely to be a focus on alignment and precision of movement, but with much more movement of the spine. Content may focus on movement concepts like giving into gravity, and use of effort; also qualities of movement.
We could do worse than refer you to this Facebook page, which references two of the great pioneers of contemporary dance.