ADC (Attack Damage Carry) is an archaic term used to refer to a champion that deals strong, continuous damage with their basic attacks and scales with attack-related stats - i.e. attack damage, critical strike chance and attack speed.
The role was retired in official contexts and replaced with Marksman, to distinguish between ranged basic attackers (including those that do not build AD, e.g. ) and the ability to carry, with melee ADCs being distributed between the Slayer and Fighter roles.
Despite retirement of the term, it remains in common usage, even among Riot employees, and generally refers to these champions: