Negative voltage means the same as positive, except the electric current caused by it would flow in the opposite direction.
As for your another question, that's just what it is: having negative potential means being more reactive than H. See, that electrode potential is not an absolute value, it can be measured only relative to something. And the general agreement is to take the standard hydrogen electrode for that "something".
Suppose you'd make an electrode out of your metal immersed in a solution of some salt of itself, couple it to standard hydrogen electrode and see what happens. If a metal is more reactive, it will dissolve, the released electrons will run to the hydrogen electrode and reduce hydrogen there. With less reactive metals, it is the other way around: hydrogen will dissolve and send the electrons running in the opposite direction, to eventually reduce the metal.