A strong fiction plot is based on a character the reader cares about overcoming a serious obstacle to an important goal through sacrificial personal growth. The underlying conflict formed by the obstacle creates emotional tension that the reader wants to see resolved. Complications are new conflicts that arise over the course of the story to extend and alter that tension. In many cases, complications arise just as a character makes a critical choice or shows important growth, forcing a whole new level or type of growth before the plot can be resolved.
It is easy to add complications to a story. The more difficult part is creating complications that further the overall story theme. A theme is the driving question the story is trying to answer. Possible answers to that driving question show up in the characters' decisions and those decisions' consequences. Thus, every complication in the theme must create situations in which the characters must make new choices that bear on the story's central theme.
Complications can extend the dramatic tension created when a character that the reader loves is unable to reach her goal. Making skillful use of complications in this way requires a good balance between meaningful tension and partial relief. Meaningless complications are those that occur arbitrarily and do not require any meaningful response or growth from the character. Similarly, a constant barrage of overlapping complications without resolution will begin to exhaust the reader, while a total resolution of conflict before the end of the story will cause a loss of interest.
Anything that could serve as the central conflict for a story can be modified to serve as a complication instead. One of the most basic complications is relational tension through insensitivity, miscommunication or refusal to forgive. Circumstantial complications can include a sudden expense or loss of resources, the unexpected return of an antagonist, or systemic barriers (such as prohibitive bureaucracy or deadly weather) arising at an inopportune moment. Internal complications include self-doubt, loss of purpose, change of purpose, discontentment after nominal success or fear of a new situation.