No story exists in a vacuum. Unless you're writing about the adventures of a gaggle of newborns, all your characters had lives before this particular plot happened. They had loves and disappointments, successes and failures. Each of them has a past. When and how do you let your reader know their stories?
Firstly, you have to know their pasts. Each writer does it their own way; some fill out questionnaires, some write mini-biographies, some just let it fly and let the character reveal themselves as the writing progresses. I seem to fall in between the latter two, I do know a fair bit about each of my characters, but as I write there are always surprises.
Secondly, how do you fit this backstory in? No one in real life will shake your hand and then proceed to tell you their life story, unless copious amounts of alcohol are involved. You learn about people over time or when certain instances occur. The smell of cookies may remind someone of their grandmother baking every Wednesday morning - or it could remind them of the scorched aroma that emanated from the oven every time their Dad tried to bake. Maybe these memories have affected their behaviour - one could have guilt that they don't bake, while another could have a fear of hot ovens. Who knows? But that cookie smell just opened the door a little wider and your reader just learned something new about your character.
There were days in your characters' lives before "Once upon a time." Give yourself time to fill in the blanks. What were their hopes? What made them happy? If they're in an unhappy relationship, there must have been a time when it was happy. What is their normal routine before you throw the events of your plot at them? And, bless their hearts, how do they react to life-shaking change? I would imagine discovering a dead body would give most people pause. So would discovering your significant other has been 'significant' with someone else.
I try to remember that no one changes overnight. It takes time. In real life, 'aha' moments are few. I try to write situations where my characters can reveal their backstories a smidgen at a time. Even best friends keep secrets from one another - and, as I've discovered, so do characters from their author.