Many a great editor have pushed authors to the limit. Is this really plausible? They ask. Wait! They wail. This character was supposed to be born in 1240 but the black plague didn't happen until a century later! Pesky little details. Yes, they are.
Developing a plausible backstory and timeline for your characters is key to making your readers true believers. Even if no one will ever read that Uncle Jimmy's folks were circus performers in the South in the early 1930's, it has a direct relationship to Uncle Jimmy's odd fear of clowns, which leads to his overreaction when Jimmy Jr. comes running in one Halloween night dressed as Bozo and Uncle Jimmy nearly loses his mind. Perhaps that's a bit extreme...but you get the point.
Timelines - especially family details and birth and death dates - can make a big difference to how you present current events for the characters in your stories. Sometimes dates really matter - like your little girl shares a birthday with her mother and that birthday lands on a Monday instead of a Saturday, causing you to have to figure out why the little girl is having a sleepover on a Sunday instead of a Saturday...to more general knowledge about how your characters real histories, ages, and home lives can influence why and how they make decisions in your plot.
Plausibility is another biggie - especially in fantasy, sci-fi, or supernatural manuscripts. If you are using fantastic elements like magic, time travel, or ghostly interferences, you need to understand the rules of the world that you created and stick with them!
Back story may have a direct and explicit affect on the current storyline, or it may just be notes you have for reference that make their way into the narrative at key moments. Backstory can give characters depth and increase interest. Introduce backstory in dialogue: "Hey, baby, when we first met, you were so free. Remember the marshmallows? You helped me...be...free. And now we're all chained up." You can also allude to backstory with flashbacks or with inner dialogue. "Are you kidding me! I didn't sign up for this! I didn't sign up for anything. Heck, I can't even write my own name without thinking about daddy. Why'd he have to give me his poor, useless name. Daddy shoulda' left before I was born instead of after. And taken his name with him." You can also use flashbacks or narrative to introduce elements of your characters' pasts.
You get the drift. So take some time and create a family tree for your characters, take them out for a drink, and really get to know them. Back it up!