Countering is when a unit automatically attacks back with their weapon if attacked by a weapon.
Counter-attacks can trigger enemy counters. The game will call it a "counter-counter" then "counter-counter-counter" and so forth.
Counter number is reduced by 1 with any action(attack,using skill) except move and lift & throw. Defend reduces your Counter number by 2, meaning that only units with stat 3 or higher get a counter while defending.
Units have a "counter" stat which is the maximum they can do per turn. Some units have 0 by default, others higher. You can spend mana to pass bills to increase this.
If you made an attack this might reduce counter by 1, meaning Counter 1 units can only counter if they moved but did not attack.
Fist weapons may increase this stat by 2.
In Disgaea 5, counter chance is 50% + remaining counter attacks x 10%.