Luke Garroway is best friends with Jocelyn Fray and, for all intents and purposes, Clary's father. During the City of Bones, he is revealed to be a werewolf and his real name proven to be Lucian Graymark. Before he was bitten by a werewolf some 15 or 16 years ago, he was actually a Shadowhunter; this is how he knows Jocelyn Fray/Fairchild. He is in love with Jocelyn, though she is oblivious of his feelings.
Luke also cares about Clary like the father she never really had. He is the only father she has ever known, and he's been around since she was little, after he tracked Jocelyn down following her escape from Idris.
Luke was also Valentine's best man in his wedding, his best friend, and his parabatai. Valentine is the reason Luke is a werewolf; they were hunting for werewoves at a werewolf camp, and Valentine left Luke to be bitten by the leader. Luke eventually went back for revenge, and became the leader of the pack after he killed the guy.
Luke is the person Jocelyn goes to for help when she becomes afraid of her husband- when she hears screaming through her walls and Valentine returning at late hours. When Luke asks Valentine about it, he disregards it as side effects from Jocelyn's pregnancy. This is before Valentine helps Luke being Changed into a werewolf.
Lucian Graymark was a follower in the Circle. He viewed Downworlders differently than Valentine, but wanted to make Jocelyn happy, so he agreed with him. Valentine took Luke under his wing when he fell behind the rest of the Shadowhunters of his age, and made him a better fighter. When Jocelyn told him of her plans to defy her husband during the Uprising, Luke helped her.
Luke, after he and Jocelyn fled from Idris, offered to get married to Jocelyn for her protection, but did not mention that it was also because he was in love with her. She rejected his offer and left him in London, refusing to find sanctuary in the Institute there and turning her back on the Clave. This is when Luke has to track Jocelyn to New York.
Lucian/Luke is described as being of average height, with brown hair and glasses worn over his blue eyes. He is mentioned to wear jeans and flannel shirts very frequently. He is very calm, is rarely seen getting angry, and is fiercely loyal to the people he loves. When Clary encounters the vampires at the Hotel Dumort, for example, Luke sends his pack to raid the clan's hotel and save Clary and Simon.