What is Convex hull trick exactly?

I was solving problems from the codeforces.ru but I couldn't solve a problem and the editorial said to use convex hull trick.

I tried to read this article about convex hull trick but couldn't understand it.

Can anyone tell me exactly what is convex hull trick?

thanks in advance.

If you have a set of lines Y_i = A_i * X + B_i, then the problem is finding the smallest Y_i for given X. Naively, you could try to evaluate all Y_i for this X and choose the smallest one. But if you want to evaluate a series of values for X, then you can better determine where the Y_i intersect and then for each interval between the intersections determine which Y_i is the smallest. Then, given an X, you choose the corresponding interval and only evaluate the Y_i that is smallest on that interval.

(Visualized by the green lines here: http://wcipeg.com/wiki/File:Convex_hull_trick1.png)