Simply put, exposition in fiction writing is anything which conveys important background information to the audience. In other words, exposition could be considered an information dump.
What could be more boring than interrupting a page of witty dialogue between protagonist and serial killer in order to describe that vital moment in the killer's life where his mother left him and his father beat him? Even if that's what made your character turn into a killer, untimely exposition can ruin a book. A reader won't have enough patience to reach the end of the story if you keep interrupting for an info dump—no matter how vital to the plot.
You can try to weave it into dialogue, but this can make your dialogue long and unrealistic. You could introduce a character who asks questions that the reader might be asking, I.e. The dumb friend, but that can sometimes be too obvious (and annoying).
Flashbacks have fallen out of vogue to some extent, but this is an efficient way to give a lot of vital information. A flashback is a scene where the character experiences a flash back to a previous time in their life, usually connected in some way to the scene at hand. This experience could be triggered by a smell or sight or something another character says. The only problem with these are that they significantly interrupt the plot and take you back into the past—whether minutes or years, it's out of the action.
Similar to a flashback, but shorter, memories look at the scene from the present, rather than experiencing it as it happened like in a flashback. Again, these could be triggered by a scent or sight or a comment. Since these are shorter, they could be considered less of an interruption than a flashback.
Perhaps the best way is to sprinkle it throughout dialogue and narrative. A sentence here, a sentence there, a little bit of setting, a little bit of backstory, but keep the focus on the action.
Day 1: Absolution
Day 2: Biography
Day 3: Confidence
Day 4: Daphne