A Counter War is a situation where two or more players are constantly striving to counter each others' cards. The cards may be Mega-Point cards, or Creativity Contingent Cards designed to modify paramaters of play.
Quite a common trick is when somebody makes a card to the effect of "If the player to your right has a card in play with a triangle on it, multiply your score by a million" is to play the "multiply all scores by -1" card. Actually, make that -2. This could them be countered by a card telling you to rip apart and reverse the effect of the previous card, which could be averted in a number of ways.