When a creature's HP is reduced to 1/4th or less of their starting HP, their survival instincts kick in. They will either attempt to flee, or fight harder. If they chose to continue to fight, they gain an extra attack, but suffers a -3 to their attacks. (That means if they have an attack that is multiple attacks, they just only gain one more.) They also lose their ability to perform reactions.
If the players wish to have a similar ability, they can have it with a slight difference. When they reduce their health to 1/3rd of their max, they can choose to get to do another attack action. However, the attacks are with disadvantage and they lose reaction until their next turn.