We love stories because they tell us what could be. They are the what-if that our brains are addicted to. As such, we crave drama in our stories. We want to know how to survive the worst possible outcome and stories give us that knowledge.
There are two ways to add conflict and drama to a story.
Internal conflict: This is all the conflict that happens inside a character. This is their thoughts, feelings, past experiences, and inner turmoil.
This is ANGST.
In Twilight, this is why Edward can't be with Bella. He has INTERNAL CONFLICT about not eating/eating her. His emotions get in the way and create tension between the characters.
As a romance writer, this is gold. Readers need this because it's usually the best reason why the hero and heroine can't be together. This is also where love stems from (as it can be a point of drama!). Internal drama is vital for romance.
External Conflict: This is what happens to the characters. These are the situations that they can't control. This is the asteroid coming to impact earth, the fire that destroys the hero's home, the dragon that is burning up the village.
In Twilight, this is the rogue vampires. Bella and Edward don't really have any control over them and what they're doing. They have to react and respond, but the conflict comes from outside of their emotions. It's also good for keeping Bella and Edward from drowning in their romantic angst. It moves the story forward.
For romance writing, external conflict is awesome for getting the plot moving. It makes the characters stop wallowing in angst and do something.
A good story will have a little bit of both. The internal conflict connects us to our characters. The reader with empathize and become emotionally attached to the story because of emotion. External conflict will keep them from getting bored.