You don't need to know all kinds of backstory detail. Where are James Bond's parents? How was James treated as a child? Who knows... that never matters to the story. The only things we know are the things that matter. So you have to ask yourself, "What matters?"
What you want to know is the characters motivações as pertains to the campaign.
What are the character's ganchos that let you, the GM, grab ahold and pull him into the story?
How does the character know the other PCs?
Meeting for the first time in the opening adventure is a difficult setup, unless you want to create an entire adventure por aí their meeting. I did this once, and it worked fairly well, but the hardest part is working around the, "I'm suspicious of him, but he has PC stamped on his forehead, so I have to trust him in the end."
Having the group establish some kind of relationship among the characters as part of character creation creates a lot of room for creating both shared backstory and motivations. Not every character needs to know every other character, but there needs to be ties that bind them together before the adventure ever starts. If the player can create just one established relationship with another PC, that creates a good starting tie.
Destino does this by literally writing each others characters into summaries of previous adventures.
What does the character quer that he is prevented from having, and what is preventing him?
This is storytelling 101... the kernel from which plot grows.
There's this type of character that burgeoning roleplayers want to create, but often don't have the chops to pull off correctly: "I just want to settle down and be a farmer."
This is a great motivation, and can make for great stories... so long as something is impedindo our hero from doing just that. I once dealt with a player with that exact motivation, who put it on me as GM to provide constant opposition without giving me any hooks. I had a really hard time keeping him from walking away from adventures, because he hadn't provided me with any reasons not to. He cared about nothing else but becoming a farmer.
It's not the GM's job to keep the character in the story, it's the player's. The would-be farmer needs a motivation that overrides his desire to buy the farm and settle down... he's hunted by the King's men for a crime he didn't commit, and he can never have peace until he clears his name.
This set of motivations have to be negotiated... they have to point toward the group story and not away from it, which means discussion amongst the group and some consensus about what direction the stories will take. If clearing his name interferes with the overall expected campaign (hanging out with these ruffians, looting tombs and the like, doesn't get him any closer to his goals), it's probably not a good motivation, because it will pull him away from the group story instead of toward.
On one level, "I want to go on an adventure and see the world," is an acceptable motivation, if it is sincere and not just an excuse for "I want to roll some dice and smash some heads." But then, if that's what the player wants, pushing him into more than that may ruin his fun. If you're a GM that uses PC motivations to craft the story, this guy may be a poor fit... that's something you'll have to navigate on your own.
Who or what shaped who the character is today?
This isn't the "who are your parents" question. Where the previous question is about "where are you trying to go?" this question is "how did you get where you are?"
The key thing is just that... the key people and events that reach through time and affect how the character interacts with the story now. This could be his parents (who beat him and made him sleep in a closet), but probably not. Maybe it's his teacher, the swordmaster who hit him, belittled him, and beat him within an inch of his life in his coming of age contest... whom the character hates with a passion, yet respects and even loves more than anyone because, like the sword he carries, the character is a weapon forged in fire and pain and would not be who he is without this "tough love".
We get here by asking two questions: Who do you want your character to be, and how did he become who he is?
Most players have a vision of their character in mind when they start play... that's usually pretty easy to get out of a player. Ask the player who the character is, how they react to situations... are they generous and kind, gruff but lovable, cold as steel and as likely to cut your throat as give you the time of day? Respond to these answers with the second question... "How did character get that way?" Who made him that way, what hard (or soft) situations or decisions in his life shaped who he became?
This is a good place for suggestions... if the player doesn't know why he's a bad-a** swordsman with nerves of steel, offer some ideas. I like to do this in the form of questions: "Did someone hurt him badly in his past? Did he learn the sword on his own or did he have a teacher? Was the teacher an important influence?" His swordmaster is only important because learning swordplay and fighting was a key part of this character's makeup. Not all fighters are going to see the sword as the key part of their life... another fighter might actually be motivated by his parents, who were killed by bandits when he was young, and this character vowed that he would never be powerless to defend those he loved again. The guy who taught him the sword was just some guy and not really a mentor.
This information is helpful on two counts: It helps inform the character's motivations so that you and the player better understand the character, (and if the stated motivations don't jibe with this background, work with the player to reconcile them) and it fleshes out the importante bits of background that can serve as hooks. These characters can appear in the future story, and even if they're dead, someone who reminds the character of his tough-love teacher is going to affect him.