What is a curvilinear curve?

Answer 1

"In curvilinear relationships, the data points increase together up to a certain point (like a positive relationship) and then as one increases, the other decreases (negative relationship) or vice versa."

A linear relation is very simple: if one variable goes up, the other goes up (positive correlation) or goes down (negative correlation).

A curvilinear relation between variables is non-linear (i.e., that cannot be described by a straight line).

Basically, anythig not linear is curvilinear.