Representation of dielectric properties by impedance spectroscopy (IS) is analyzed carefully in this paper. It is found that IS is not a good tool to describe a uniform system because a pseudo relaxation peaks exists at low frequency limit corresponding to direct current (DC) conductivity and two relaxation peaks appears simultaneously corresponding to one relaxation process for a high loss system with tand>1. However it is very convenient to describe a multiple phase system with IS. When dielectric properties are shown by Cole-Cole equation, only one Cole-Cole arc appears for one phase in IS, therefore it is very easy to distinguish different phases from each other. Especially, since pseudo relaxation exists at low frequency limit for each phase, the location of a certain relaxation process can be deduced by IS without any uncertainty. Furthermore, when dielectric properties are shown with specific impedance spectroscopy (ISI), the information of microstructure can be obtained conveniently. Based on the theoretical results above, dielectric properties of CaCu3Ti4O12 (CCTO) ceramics with giant dielectric constant (GDC) are investigated. Microstructure of CCTO is obtained by dielectric spectrometer and the origin of GDC is found to come from pseudo relaxation of grain.