What does a higher half cell potential mean? I was taught in class that a positive large half cell potential generally meant that the reaction was more favorable.  What exactly does this mean?  Doesn't a reaction with potential 4V need a greater input of energy to occur? Meaning that a lower electron cell potential would occur first and is therefore more favorable?

Also how why does Zn(II) +2e- ---> Zn favor the left side of the reaction?  Shouldn't Zinc naturally tend towards being neutral?
That's not quite correct.

Half-reaction potentials are only really meaningful when you complete the redox pair, that is, you must have an oxidation and reduction reaction. The sum of the potentials is the potential for the full redox reaction at standard concentration and state. In that sense, the more positive either of the potentials is, the more favorable the overall reaction will be.

There is no preference for a neutral species in general. If you put sodium in water, the electron is quickly liberated and the end products of hydrogen and sodium ion are much more favored than the reactants of water and sodium.