A strong electrolyte completely dissociates into ions in a solution. A weak electrolyte dissociates only partially into ions.
The dissociation of acetic acid in water can be represented by the following equation:
$$CH_3COOH_{(aq)} + H_2O_{(l)} \rightleftharpoons CH_3COO_{(aq)}^- + H_3O_{(aq)}^+$$
At equilibrium, only a small fraction of acetic acid molecules are dissociated, so the concentration of ions remains low, which means that acetic acid is a weak electrolyte.