One Piece's title refers to a treasure left behind by Gol D. Roger, the late pirate king. He is frequently described as the strongest pirate to ever exist, and his execution only possible due to his consent. Only a few characters in the series are confirmed to have traded blows with Roger and walked away alive. Chief among them are the deceased Yonko Whitebeard and Luffy's grandfather, Vice Admiral Monkey D. Garp.
Garp has a long history with both Whitebeard and Roger. He and Roger teamed up against the Rocks Pirates (of which Whitebeard, Big Mom, and Kaido were all members) in a battle known as the God Valley Incident, which led to the dissolution of that crew. The Rocks Pirates were targeting the World Nobles, and thus Garp's actions in the battle earned him the title of "Hero of the Marines". Garp would fight and attempt to capture Roger numerous times after that. Prior to Roger's execution, Garp agreed to care for his son, Portgas D. Ace, raising him along with his grandson Luffy.
Garp's Powers
The mere fact that Garp traded blows with some of the most notorious pirates ever and lived to tell about it speaks to his tremendous strength. However, most of this history is spoken about but not directly shown throughout One Piece, and thus the exact nature of Garp's abilities are poorly explained. All of Garp's exploits so far involve raw physical power and durability. He took no serious damage from a punch thrown by Luffy in Gear 2, despite it sending him flying, and barely noticed when the former Marine captain Axe-Hand Morgan slashed him.
Garp has been seen throwing cannonballs with his bare hands at speeds that surpass those that they reach when fired, and effortlessly swung a giant iron ball attached to his ship by a chain. When it comes to strength, however, Garp is especially renowned for his punches, granting him the epithet "Garp the Fist". Garp put this strength on full display by punching Marco, Whitebeard's right-hand man, and sending him flying while the latter tried to save Ace from execution at Marineford. Garp managed to do this while Marco was in the form of a phoenix and capable of near-instant regeneration, something Garp's superiors, the Admirals, struggled to counter. Marco is also a frighteningly powerful pirate with a bounty of 1.374 billion berry.
Is Garp the Strongest Marine?
Garp's reputation belies his comparitively low rank of Vice Admiral. In reality, this is due to his refusing to be promoted to Admiral on multiple occasions. Garp is easily the most powerful Vice Admiral in the Marines, and rivals or exceeds the power of the known Admirals and Fleet Admirals. After then-Admiral and future Fleet Admiral Sakazuki (also known as Akainu) killed Ace, Fleet Admiral Sengoku held Garp down to prevent him from killing Sakazuki in revenge. The fact that he did this illustrates that Sengoku genuinely believed Garp had the power to kill or seriously injure Sakazuki.
Sengoku and the mysterious Kong are the only known Marines who may genuinely match or exceed Garp in strength, making him a contender for the strongest in the entire force. Garp's importance in One Piece goes further, however, in that despite his loyalty to the marines, he was responsible for raising four major threats to the World Government. Aside from Luffy and Ace, who eventually became a member of Whitebeard pirates, Garp is also the father of Monkey D. Dragon, Luffy's father and the leader of the Revolutionary Army, and rasied its second-in-command, Sabo, alongside Luffy and Ace. Garp had originally wanted all of them to become marines, and it is a point of shame and tragedy for him that they didn't, and are therefore his enemies.
Garp's role in the story can be expected to expand before One Piece draws to a close. As he had to do with Ace's execution at Marineford, he will likely be forced to confront Luffy and possibly Dragon before the series comes to a close as a member of the Marines. When he does, he may show off enough power to justify his monstrous reputation.