A counterexample is any example that disproves the conjecture, or the statement. In other words, we need an example that does not follow the claim that three coplanar lines always make a triangle.
Coplanar lines are lines on the same plane. A plane is a flat, 2-d surface that extends infinitely. You can imagine a really big table.
One counterexample is three lines on the plane that are parallel to each other. Since they won't intersect, they won't form a triangle.
Another counterexample is two lines that are parallel and one that intersects, and it won't form a triangle because two lines are parallel.