Think of the character's childhood. Was it happy? Was the family loving? What were her family's socioeconomic circumstances?
Consider the time period of your plot. For example, if your story is set in the late 1700s or early 1800s and the character's family is poor, your character probably would not have much schooling. Nor would he have the opportunities for advancement or leisure that wealthier people have.
Imagine what the family might have expected from the character as she was growing up. If the family is lower class and lives in present times, determine whether the family would have pressured the character to succeed and rise above her circumstances. Explore how the character would respond. Would she become an overachiever or a rebel, deliberately doing the opposite of what the family desires?
If the book is historical, this issue can be explored in various ways. If the character is female, delve into whether she is expected to marry up and thus advance the position of her family. If the character is male, perhaps the boy or young man joins the armed forces during wartime as a means to advance his own position in society.
Think about the character's interests. Does she paint, play an instrument, read or do charitable work? What is her vocation?
Read biographies of historical or notable people. You can find out what motivates various people and how people choose to live their lives. Reading biographies can be especially helpful when writing a historical novel, because they can better help you portray the world in which your character lives.
Read books for writers on developing characters and their traits.
Write your character's biography based on the information and impressions you have gathered. The more of a backstory you can provide for your character, the more interesting your character will be and the better your story will be for your readers.