From the Super Mario Wiki
In Mario Power Tennis, there are two types of Power Shots; Offensive Power Shots and Defensive Power Shots. All players have their own distinctive power shots. The offensive power shot is used when the ball is near the player. These come with special effects to confuse the opponent(s). Defensive shots are used when the ball is out of the player's reach. These shots are very helpful by returning shots that couldn't normally be saved. In fact, Defensive Power Shots can also negate the added effects from Offensive Power Shots.
Power Shots are also a prominent feature in Mario Tennis: Power Tour, where part of the game's story revolves around the player and other characters in the game's RPG mode developing Power Shots. Power Shots can be earned by completing minigames at the Tennis Academy Training Center, and the player can then assign any offensive or defensive Power Shot available to them, to Ace or to Clay. Additionally, there is a Power Shot under the name Power Shot in the game.
In Mario Superstar Baseball, power shots are used in either pitching or batting. if the player uses one when the player's pitching, the player will throw a ball that does varying things, making it hard for the opponent to hit. If the player uses it offensively when the player's hitting, the player will hit the ball in a way that is hard to catch for the CPU to catch. In Mario Super Sluggers they were most likely replaced by Star Swings and Star Pitches.
Power Shots also appear in Mario Golf as a stronger version of a specific club. There is a meter starting at six that decreases if shots are made that don't have full power. Some characters have special effects when a perfect power shot is executed, such as Mario's golf ball becoming a fireball.