A curvilinear relationship is when one variable increases another does as well, but at one point it stops, and only one variable continues to increase and the other decreases. On a graph, this relationship looks like an upside-down “U”, which is why its also called an inverted-U graph. Another type of curvilinear relationship is when one variable increases and another decreases at the beginning, but they stop at a certain point, whereby both variables continue to increase after. This results in a normal upside “U” shape.
Think of going on a date. As you both meet, you’re having a fun time, getting to know each other and laughing. You’re both going higher on the happiness scale. But then she keeps laughing. At every little thing you say, even if it’s serious. At that point, you’d probably start souring on your feelings about the date, while that psychopath keeps getting happier and happier. This would represent a curvilinear relationship in an inverted-U pattern.