Hagrid is the groundskeeper at Hogwarts, but, man, he's so much more than that. He's pretty much the friendliest, most trustworthy, and most loving authority figure at Hogwarts. He previously attended Hogwarts and was expelled during his third year. While he's not allowed to do magic anymore, he clearly knows how; Harry notices the special way Hagrid treats his umbrella. Hagrid means well and tries to keep secrets, but he's constantly letting things slip. He's kind of an open book in this way; he gives away the secret of how to get past Fluffy to a stranger in the Leaky Cauldron way too easily.
Hagrid can also be seen as the gatekeeper between magic and Muggle worlds, at least as far as Harry is concerned. It's a young Hagrid who safely brings the baby Harry to the Dursleys via magic motorcycle, and cries when he has to leave Harry there. It's a mature Hagrid who arrives on Harry's eleventh birthday, like some sort of hairy fairy godmother, and reveals to Harry who he really is. Hagrid is really angry about the way the Dursleys have treated Harry and that fact that they haven't told him the truth about his parents and the wizarding world. Hagrid takes this duty upon himself and fills Harry in on the things that have been hidden from him.
Hagrid is Harry's friend – and soon, he's also friends with Ron and Hermione. He invites them all to tea at his house on their days off, and he tells them the secret of his baby dragon. Hagrid's got a special relationship with animals – he's like a magical animal whisperer. He's got an everyday dog, Fang; he provides Dumbledore with Fluffy, the three-headed monster dog; and he's crazy about dragons. He also gives Harry a pet as his first-ever birthday present (Hedwig the snowy owl), and Harry is blown away by the idea that somebody would act so generously toward him. We already knew that Hagrid's a big softie, but it's especially sweet when he gives Harry another present: the wizard photos of his parents. This gift shows real sensitivity and love.