The graphene speaker was made by depositing graphene-oxide onto poly vinylidene fluoride (or PVDF) and then reducing it to create a graphene film (this is actually a new method to develop graphene films). So basically this speaker is made from PVDF sandwiched between two graphene electrodes. When an electrical current (from the sound source) is applied, the converse piezoelectric effect causes the PDVF film to distort - and thus sound waves are created.
The researchers say that Graphene speakers will be cheaper and very power efficient compared to other types of speakers. There is still a lot of work to be done, and the research group is currently developing an improved bass response.
More info: http://www.rsc.org/chemistryworld/News/2011/July/08071101.asp