Questions about exceptions use

I am still a beginner and I do not really grasp the purpose of exceptions in a program.

When you throw an exception, you basically skip a (small or big) part of your program, so one of my questions would be : should an exception leads to the end of the program ?

Also, suppose we have a class Rectangle. It would be define by its length and its height like this :

#include <iostream>

using namespace std;

class Rectangle {
public:
    Rectangle(double length, double height)
    {
        if (length > 0 and heigth > 0) {
            length_ = length;
            height_ = height;
        }
        else {
            // Throw an exception ? Use a convention ?
        }
    }
    // other methods
private:
    double length_;
    double height_;
};

int main() {
    // do stuff

    return 0;
}

However, it would not make much sense to have a negative length or height. So should I throw an exception in the constructor ? Should I use an arbitrary convention and take their absolute value ? Should I prevent the user in the main() from passing negative arguments ?