Some games allow a monster to strike back at an opponent while they are in the process of attacking. This is quite a gamble, as the probability of it working is much less than a normal attack, and if it doesn't work, extra Damage is done. However, if it works, massive amounts of Damage are done to the opponent.
The concept of the Counter Attack was first introduced in Monster Rancher Advance 2, but has continued in several other games.