Water levels in piezometers tell us the state of energy at points in the subsurface. From this information we deduce equipotential lines and flow directions as shown in the upper portion of the diagram. The schematic sketch also shows the changes in total head h, gravity head or elevation head he and deformation head hp along an assumed flowline. Groundwater typically does not flow horizontally.
If you wish to learn more about groundwater flow against Pressure Gradients, the information can be found in K.U. Weyer's 1978 paper "Hydraulic forces in permeable media", Mémoire du B.R.G.M., vol. 91, pp.285-297.