Carbon materials have unveiled outstanding properties as membranes for water transport, both in 1D carbon nanotube and between 2D graphene layers. In the ultimate confinement, water properties however strongly deviate from the continuum, showing exotic properties with numerous counterparts in fields ranging from nanotribology to biology. Here, by means of molecular dynamics, we show a self-organized inhomogeneous structure of water confined between graphene sheets, whereby the very strong localization of water defeats the energy cost for bending the graphene sheets. This leads to a two-dimensional water droplet accompanied by localized graphene ripples, which we call "dripplon." Additional osmotic effects originating in dissolved impurities are shown to further stabilize the dripplon. Our analysis also reveals a counterintuitive superfast dynamics of the dripplons, comparable to that of individual water molecules. They move like a (nano-) ruck in a rug, with water molecules and carbon atoms exchanging rapidly across the dripplon interface.