AC (alternating current) and DC (direct current) electricity differ due to the nature of the source of electric potential difference driving the current in the circuit.
Batteries are an example of a source of DC. The potential difference from a battery is steady; it produces a steady electric field in the wires used to connect the circuit, and the electrons drift with an average drift speed in one constant direction.
Household outlets are an example of a source of AC. The potential difference from an outlet oscillates from positive to negative (with a standard frequency of 60 cycles per second); it produces an oscillating electric field (i.e. repeatedly changing directions) in the wires used to connect the circuit, making the electrons drift back and forth.