Reduction always happens at the cathode, and oxidation always happens at the anode. Chemistry students often remember this with the mnemonics RED CAT, reduction at the cathode, and AN OX, oxidation at the anode. The cathode’s electrical charge depends on what kind of cell it is in.
In a galvanic cell, which generates electricity spontaneously like a discharging battery, the cathode is the positive terminal. In an electrolytic cell, which uses outside electricity to force a non-spontaneous reaction to occur, the cathode is the negative terminal, because it connects to the negative terminal of the power source driving the reaction.
This function-based definition, not a fixed electrical charge, is what actually defines any cathode. Conventional current flows into the cathode from the external circuit, while electrons flow into the cell there and are used up by the reduction reaction on its surface. In household batteries, the cathode is typically labeled with a plus sign, since batteries function as galvanic cells while providing power.
The word cathode comes from Greek roots meaning a way down, reflecting the historical idea of current flowing down into the electrode.