The Power Attacker effect is exclusive to creatures, although there are Spells and Cross Gears which can grant it to creatures. It grants a creature additional power when attacking, enabling them to deal with a larger variety of creatures as well as making it more difficult to block the creature unscathed. It does not affect the opponent as power has no use other than battling creatures.
However, Power Attacker doesn't trigger when a creature is attacked. Therefore, a creature that has Power Attacker and low base power is extremely vulnerable to being attacked and destroyed by a stronger creature.
Power Attacker has a variation; Infinity Power Attacker, which grants the creature that has it infinite power rather than a fixed power increase. This version of Power Attacker can be considered a weaker version of Win All Battles and it cannot defeat a creature with said ability.
Early Power boost spells and creature effects tend to use Power Attacker to give creatures additional power instead of an actual power boost. (e.g. Aura Blast, Galsaur)
The latest reminder text for Power Attacker reads;
Power Attacker +N(While attacking, this creature gets +N power.)
Multiple instances of "Power Attacker" stack. For example, a creature that has 1000+ power which has a "Power Attacker +1000" and a "Power Attacker +2000" ability gets +3000 power while attacking, resulting in a total of 4000 power (1000+1000+2000).
When a Shield with a Shield Trigger ability is broke, the creature with the power attacker ability will still be considered having the same amount of power when attacking until the Shield Trigger is used. (For example, a Fire Sweeper Burning Hellion who breaks a shield with Tornado Flame will be treated as having 5000 power instead of the usual 3000.)