What is Redox couple and half-equation?

An oxidant and the reductant it becomes by gaining electrons form a redox couple, written Ox/Red with the oxidant first: $\ce{Cu^{2+}}$/$\ce{Cu}$, $\ce{Zn^{2+}}$/$\ce{Zn}$. The exchange of electrons inside a couple is described by its half-equation,

balanced in atoms and in charge, for instance $\ce{Cu^{2+}(aq) + 2e- <=> Cu(s)}$. The double arrow says that the exchange can go either way.