A-Counter, otherwise known as "Alien Counter", is a type of counter associated with the "Alien" archetype. Certain card effects depend on these to exist on opponent's monsters to work. The majority of the time, when an "Alien" monster battles a monster that has an A-Counter, the monster with the A-Counter loses 300 ATK and DEF during damage calculation only.
However for this ATK/DEF reduction, you need a monster on the field with an effect that specifically mentions this ATK/DEF decrease, as it is not an inherent condition for A-Counters. The benefit of this is that the ATK/DEF reduction is cumulative with more monsters that have that effect on the field, as supported by the rulings for "Alien Grey".
Lore-wise, A-Counters take the form of "Corruption Cell "A"", which resembles a gelatinous blob of flesh with a tubular "mouth" and a tail. "Interplanetary Invader "A"" is also an A-Counter, apparently having evolved legs and the ability to control minds without the need of another "Alien" monster.