Counterfeiting in poker is when a ‘counterfeit’ card comes that doesn’t improve a player’s hand, but instead, makes it worse. It doesn’t change the value of a player’s hand it just makes it difficult to still have the best hand.
Examples of counterfeiting in Texas Hold’em.
You have two-pair on the turn with A-3 on a board of J-3-A-5 the river card is another J meaning the paired board likely gives your opponent a better hand if they got to the turn with an Ax hand since they will have you outkicked. You have been counterfeited, and in situations like this you just want a cheap showdown. When facing a big bet from your opponent you should just fold.
Another example of poker counterfeiting is when the board is double paired. ie. 8-8-9-3-9 and your holding a pocket pair lower then the board pairs such as 6-6. On the turn you still likely had the best hand against an aggressive opponent, but the river card means any player who is holding a card higher then a 6 will win the pot.