What is Electrode potential, standard potential?

The standard hydrogen electrode is a platinum electrode in contact with hydrogen gas at $1\,\mathrm{bar}$ and an ideal solution of $\ce{H+}$ of activity 1. The electrode potential $E$ of a half-cell is the voltage of the cell formed with the standard hydrogen electrode on the left: $E = V_{\text{half-cell}} - V_{\text{SHE}}$. When every species of the couple has activity 1, it is the standard potential $E^\circ$ of the couple, a constant at a given temperature.