Well, usually they have complex storylines. For example, they might have multiple plot threads running simultaneously. In 'Infinite Jest' by David Foster Wallace (if we consider it in a graphic novel - like sense in terms of complexity), there are numerous sub - plots that all eventually connect in some way.
In a story, complications are the problems or challenges that make the plot more interesting and prevent things from going smoothly for the characters.
One possibility could be that in the fanfiction, the labor complications might be caused by a magical curse placed on Hermione during her pregnancy. Draco, being by her side, could use his knowledge of dark and light magic to try and counter the effects. He might have to make difficult choices between following traditional pure - blood magic practices and using Hermione's more liberal magic knowledge to save her and their unborn child.
One common complication is capsular contracture. This is when the scar tissue around the implant tightens, causing the breast to feel hard and look misshapen. Another issue can be implant rupture. This might not be immediately obvious and could lead to leakage of the implant material inside the body, which can cause pain and other health problems. Also, some people experience infections after breast implant surgery, which can be very serious and require removal of the implant.
The labor complications could be such that it forces Draco and Hermione to seek help from the wizarding hospital. There, they encounter different magical treatments and potions. Some healers might be hesitant to treat Hermione because of her Muggle - born status, but Draco would fight for her rights and proper medical attention.