Without conflict, there is no story. It doesn't get any simpler than this. As someone who avoids conflict in real life, sometimes it's not that easy to throw trouble in my characters' way. After all, I love my characters. I introduced them to each other. I want them to get their happily-ever-after ending.
But a boy-meets-girl, boy-gets-girl story would not only be short, it would be a little boring as well. And we never want to bore our readers.
There are two kinds of conflict (obstacles to your characters goals and desires): External and Internal.
External conflicts are obstacles over which the characters have no control, but which affects their lives and the decisions they make. The heroine who is a suspect in the hero's murder case. The father who doesnt think the hero is good enough for his little girl. The hero who is a Union soldier and the heroine is a Rebel spy. External conflicts moves the plot along.
Internal conflicts are emotional and are a product of the character's background and personality and experiences. In order for them to be resolved, the character needs to learn something about themselves and/or each other. In the character driven stories that I write, the internal conflict is what drives the story. It's the main conflict in the stories that I write, the last to be resolved. Everything else is complication.
In the story I've just started, the heroine is newly divorced, her children have left home and she's embracing an independence she's enjoying for the first time in her life. Then she begins to fall for the hero, at a time when she doesn't want a man in her life, so she wants to take things really slow. The hero's wife died a few years ago and so when he falls for the heroine, he doesn't want to waste any time, because he knows how precious time is. Conflict!
I'll have to let you know how it all works out, but you can be sure these two will end up perfect for each other, even if life isn't always perfect.
I love stories where the character's change because of each other, where dealing with the conflicts, in the end, is simply a way to grow and to show their love for each other. And when I see characters strive to make things work out, then I cheer them on, and I believe in that happily-ever-after ending.