The Stress Meter is a sort of super bar that was first implemented in Power Instinct 2 and has become something of a staple of the series. Like most power bars of its ilk featured in fighting games today, it enables the fighters to use devastating Super Attacks. The difference, however, is that the Stress Meter fills up when the player is hit by attacks or when their moves are blocked by the opponent.
However, the Stress Meter would not fill up if a character were ever to transform during battle, regardless of whether or not their attacks were blocked or hit, and would remain as such until the transformed character reverted back to their normal state.
In Power Instinct Matrimelee, the Stress Meter was given an update. The Stress Meter could be filled up to three levels, and taunting during battle can fill it up considerably if the player isn't attacked before it can start doing so. The levels enable warriors to use Stress Shots (1 level), Ippatsu Ougis (2 levels), and Kinjites (3 levels), as well as special counterattacks that use up a level.
The Stress Meter was dropped after Matrimelee, and replaced with a more genericish Super Bar since Bonnou no Kaihou. Regardless of the type of meter it was, whenever the bar filled up, the Stress Flame would burst out of the character, so there is much more to the benefit than just gaining a level, or the ability to use a Super Attack.