Negative pressures occurrence in EPANET means that in a given point the pressure within your piping is below the atmospheric pressure, assumed around 1 bar. This is, however, an unlikely situation in an existing system, as it is highly likely that an air vent or even an open faucet is allowing air to enter, causing an abnormal and hard to model situation that reduces the flow in ways that are hard to evaluate.
A system's curve represents the amount of head you need to cause a certain flow through the piping system in permanent regime. There are many workarounds to obtain this curve from Epanet, but its simulation results do not give this curve. What it really does for you is calculating the balance point to a given set of conditions (demand, diameters, rules, headloss coefficients, pump curves and etc...) using a model.
This way, you can say (roughly) that the result shows you the obtained flow to a given pressure, and not the pressure needed to obtain a given flow.