Link

Despite being the hero of the story, Link is actually a simple goathearder who enjoys the simple things life has to offer - like fishing and roughhousing with his childhood companions. He was raised in Ordon Village, presumably by Bo, and has a close, meaningful relationship with Ilia. A relationship that echoed throughout the course of Twilight Princess and served as the foudation for most of Link's adventure.

For the first time ever, Link prepared to leave his hometown to deliver a sword made by his mentor, Rusl, to Princess Zelda herself. Though destiny seemed to have other plans for Link, as it often does when it comes to green clad heroes, and he is soon faced with the abduction of Ilia and all the children of Ordon Village. He is later met with the strange imp-like creature, Midna, and, even though he's unsure of her intentions at first, becomes her partner in order to save his friends.

It was obvious that when Link walked into Telma's Bar he was broken-hearted to discover his best friend for sixteen years couldn't even remember his name; there was not even a sign familiarlarity in her eyes at all. Telma reveals to him that Ilia has amnesia and can't even remember her own name. Distressed by everything that's happened to Ilia in his absence, Link lends his courage to Ilia and helps her in every way he can in hopes that she will remember him again. He leaves her in the care of Renado, a shaman in Kakariko Village, while he continues to aide Midna and find a way to restore Ilia's lost memories.

He returns later carrying an item she had left behind in the Hidden Village - the horse charm - and all of her memories come rushing back to her as she holds the charm in hand. However, it is not so much the charm that cures her amnesia, as all the feelings associated with it. Ilia gives the horse charm to Link as others clear the room, presumably to give them some alone time; she tells Link she made the item especially for him and was going to give it to him before he left on his journey to Hyrule, and then promises to wait for him until his return.

It's obvious Link shares a strong connection with Ilia, a connection which rivals that of his close partnership with Midna, a connection Midna herself even recognizes. Link is a changed man by the story's end and appears to be struggling to find himself. This is why I believe he leaves his home and a sad Ilia behind. Link has been a ranch hand his whole life and his adventure opened up new worlds to him, now that he's experienced such life changing events I imagine it would be difficult for him to simply go back to how things were. ...Even if he wanted to, the world is a different plance to him now and he needs to know how he fits in. Ilia, being a supportive friend, understands and continues to keep her promise. Whether or not the relationship between Link and Ilia extends beyond a close friendship is unknown, but the posibility is definitely there.