We investigate dynamic heterogeneities in liquid water by performing molecular dynamics simulations of the SPC/E model. We find clusters of mobile molecules. We study the temperature and time dependence of the cluster size and find that clusters grow as temperature decreases and have a maximum size at the time scale corresponding to the escape of the molecules from the cage formed by neighboring molecules. We relate the average mass n* of mobile particle clusters to the diffusion constant, D, and the configurational entropy, S-conf. We find that n* can be interpreted as the mass of the "cooperatively rearranging regions" hypothesized in the Adam-Gibbs theory of the dynamics of supercooled liquids. In the context of the potential energy landscape (PEL) approach, the diffusion of molecules is related to the change of basins. By studying the dynamics of the system on the PEL, we identify clusters formed by the molecules with large displacements as the system visits consecutive local minima on the PEL. We relate the changing of basins with the restructuring of the hydrogen bond network.