Answer is: because this compound in water dissociates on cations and anions and ions in solution conduct electricity.
Chemical dissociation of acetic acid in water:
CH₃COOH(aq) ⇄ CH₃COO⁻(aq) + H⁺(aq).
When we put electrodes (cathode and anode) in acetic acid solution, positeve and negative ions migrate to electrodes.
Negative acetate ions go to positive electrode and gives electrons to electrode.
Positive hydrogen ions go to negative electrode and gain electrons.
