What is Anode, cathode?

Example 47.12 (Water, split)

At the cathode: $\ce{2H2O + 2e- -> H2 + 2OH-}$; at the anode: $\ce{6H2O -> O2 + 4H3O+ + 4e-}$. For four electrons, two molecules of dihydrogen and one of dioxygen, while the ions $\ce{H3O+}$ and $\ce{OH-}$ formed at the two electrodes recombine into water: overall $\ce{2H2O -> 2H2 + O2}$, the reverse of the combustion of hydrogen, which needs energy to happen.

Example 47.14 (Refining copper)

Impure copper from the smelter is made the anode of an electrolysis cell in copper sulfate solution, and a thin sheet of pure copper the cathode. At the anode copper dissolves, $\ce{Cu -> Cu^{2+} + 2e-}$; at the cathode pure copper is deposited, $\ce{Cu^{2+} + 2e- -> Cu}$; the impurities fall to the bottom or stay in solution. A current of $100\,\mathrm{A}$ for $24\,\mathrm{h}$ carries $Q = 100 \times 86400 = 8.64 \times 10^{6}\,\mathrm{C}$, that is $n(e^-) = 89.5\,\mathrm{mol}$, which deposits $89.5/2 = 44.8\,\mathrm{mol}$ of copper: $2.84\,\mathrm{kg}$.