The more positive something's electrode potential is, the more 'reactive' it is.
In the reaction you gave as an example, copper ion gaining electrons to become copper metal has a potential of 0.337. The dissociation of water has a potential of -0.83. Therefore, copper would be reduced.
The potentials listed are reduction potentials, because in these cases, the substances are gaining electrons, and gaining electrons is reduction (I'm sure you already knew that, but I wanted to make sure). If you want to know the oxidation potentials, you have to reverse the reaction and the potential.
For example, Cu2+ going to Cu with no charge takes 0.337, as I already mentioned.
So Cu going to Cu2+ would have a potential of -0.337. The formation of water would be 0.83, so water is more likely to be oxidized than copper.
Understand?