They make the story more interesting. Shorn of its complications, you get plots like "The man and woman met, fell in love and married." or "A person was killed, the police were called in and immediately identified the killer" or "The soldiers were ordered to take the enemy's position, which they did."
A problem for a main character
Minor conflicts (problems) are called Complications. A Complication causes change in the course of the story.
The crisis in the Lightning Thief is when the bolt was stolen from Olympus, which led on to the beginning of the Lightning Thief's story.
it is exposition and complication
an outline of characters and setting which prepares the reader for the conflict.
A solution in the plot of a story means a conclusion to the complication.... or a happy ending. E.g. Fred has an itchy head, the solution would be that he scratches it =D
Complication
the complication
Complication is a twist in the plot where some new development is added. It leads to rising action or growth in the story.
Complication, climax, resolution, exposition
Complication
The complication is the central problem or conflict that arises in a story, usually as a result of the main character's actions or decisions. It creates tension and drives the plot forward by presenting obstacles that the characters must overcome in order to reach a resolution.