Monkey D. Garp is a Marine hero, who was famous for cornering the late Pirate King, Gold Roger numerous times in his career. Garp is considered by Whitebeard as one of the few people that know the seas from the time of Gold Roger.
Early on in Luffy's life, he was trained by Garp to become a strong Marine. Luffy was thrown into valleys, left alone in dangerous forests, and tied to balloons over high altitudes, all for the sake of making him stronger. After this he left Luffy and Ace in the care of Dadan.
Garp is first introduced in Koby's mini-series as the Marine Officer in charge of escorting Captain Morgan. However after falling asleep, Morgan makes his escape by striking Garp and taking Helmeppo as a hostage, fleeing on a small dingy. Garp then wakes up unharmed, apparently breaking a cannon in the process of waking up.
When Koby begs to chase after the two, Garp allows Koby to pursue them. Upon the boys' return they offer themselves to be punished, but Garp instead proposes a different course of action. He states that the pair of them are nothing but trouble and the only way to ensure they still in line is that he takes charge of the pair. He takes them back to Marine HQ where he begins to train them to become great Marine Officers.
(Source: One Piece Wikia, Wikipedia)
