Despite childhood dreams of being a grocer or a fighter pilot, young Rupert Giles was destined to be a Watcher, as his father and grandmother were before him. When Buffy heard this story, she assumed that Giles was thrilled by the news, but it wasn't until later that we discovered the lengths to which he went to try to escape his destiny.
At 21, Giles dropped out of Oxford, adopted the name 'Ripper' and took up with the worst crowd that would have him. They practiced magick as a way to get high, taking turns inducing possession by a demon called Eyghon, but things went horribly wrong one night when it completely took over their friend Randall. They tried to exorcise Eyghon, but he was too strong. And despite their best efforts, Randall was killed. Though he never said it implicitly, it seems understood that this tragedy was what drove Giles back to the Council, to accept his Calling.
* This next part of Giles' backstory is courtesy of the Buffy comics...
After Merrick (Buffy's first Watcher) died, two men were next in line for the position: Willem Bryardale and Rupert Giles. Scenes of Giles procuring spell ingredients from questionable sources suggested that he was attempting to use dark magick to sway the Council's vote, and a younger colleague (does the name Wesley ring a bell?) brought Giles' activities to the Council's attention. Rather than deny the charges, however, Giles explained that he was using this dangerous magick not to influence the Council but to expose Bryardale's efforts to do so. But when Giles called upon some seriously verboten mojo in order to defeat a rampaging Bryardale, Travers ruled that before Giles could become Buffy's Watcher, he would have to endure a trial called the Blackshed. That life-threatening trial brought him literally face to face with Ripper, presumably to rid himself of the passionate anger (and disdain for authority) that fueled his younger self. But Rupert decided that in order to serve his Slayer and be the man he needed to be, then Ripper would and should always be a part of him.
After Giles received his assignment, we actually met his father (whose name wasn't given). Rupert is satisfied with his achievement, but his father is decidedly not...
Giles Sr: Don't be too proud for surviving the Blackshed, Rupert.
Rupert: Though none before me ever have?
Giles Sr: The fact that you even had to take the test should be a source of embarrassment to you. It certainly is for me. You should have stayed at the museum, son. This job will be the death of you... or worse, the death of us all.
So yeah, two bits of information there. One, Giles did in fact work in a museum before going to Sunnydale. And two, his father is/was a jerk.
After arriving in Sunnydale, Giles became the librarian at SHS to serve as Buffy's Watcher. She rejected the Council's methods, doing things her own way, but the two made an excellent team. Not long into their partnership, Giles found himself at odds with the school's computer teacher, but Jenny's skills and resources made her a welcome ally. Her flirtatious charm soon won Giles over, and the two of them began dating. But several significant bumps in the road conspired to keep their relationship from progressing, despite their obvious attraction.
Resolving to give each other another chance, Jenny planned to meet Giles at his flat one night, but Angelus murdered her, snapping her neck. He left Jenny's body for Giles to find, and in his rage and grief, Giles attacked Angelus with a flaming baseball bat, determined to kill the vampire or die trying. Buffy intervened, dragging him out of the burning factory. His rage subsided, but it was a long time before Giles was really himself again, especially after Angelus abducted him to force the secrets of Acathla from him. An unlikely alliance between Buffy and Spike spared Giles' life, but it couldn't prevent the hours of brutal torture Giles endured at Angelus' hands.
After Buffy returned from L.A., Giles found himself in the unheard-of position of being Watcher to two Slayers at once. It wouldn't last, however, because Giles' refusal to allow the Cruciamentum to pass without coming to Buffy's aid saw him fired from the Council. He stayed on, continuing as Buffy's Watcher at her insistence, even though the position was no longer official. He would lose his secondary job not long after, on Graduation Day, when the library (along with the rest of SHS) was blown up to stop the Mayor's Ascension.
With the younger Scoobies all beginning college or jobs, Giles found himself with more free time than he knew what to do with. He enjoyed a couple of romantic visits from a friend named Olivia, but the danger in his life proved too scary for her. He considered returning home to England, since it appeared that Buffy no longer needed him, but her words to the contrary convinced him to stay. Soon after that, he bought the Magic Box, which became the new Scooby base of operations - and had a very healthy profit margin. Then when Buffy rejoined the Council (or more properly, allowed them to rejoin her), she demanded that Giles be reinstated as her official Watcher.
Once again, the status quo wouldn't hold. Buffy sacrificed herself to save the world (she does that sometimes), leaving Giles to train the Buffy-Bot in order to keep up appearances. But an innocent question from her convinced Giles that it was time to return to England. He wasn't there very long, however, when news of Buffy's resurrection brought him back to Sunnydale. He was overjoyed to see her alive, but that joy didn't last in the face of Buffy's obvious depression and self-destructive behaviour. He returned to England again, hoping she would be prompted to take care of herself in his absence, but things only got worse.
Imbued with an entire coven's magick, Giles returned in spectacular fashion to help stop a grieving Willow's murderous rampage. This effort nearly killed him, but he survived, bringing Willow back to England to heal and to learn how to control her powers. Before he could contemplate rejoining the others, however, an all-out assault by the forces of The First Evil saw Rupert combing the globe for surviving Potential Slayers. He brought them to Sunnydale, effectively becoming the Council itself when an explosion in London wiped out their numbers.
Along with the others, he helped to close the Sunnydale Hellmouth, ending The First Evil's assault. What he'll do next is anyone's guess, but with a planet full of newly called Slayers, a Council to rebuild, and another Hellmouth active in Cleveland, there's still plenty of work to be done.