You just have to define that Animal implements Comparable<Animal> i.e. public class Animal implements Comparable<Animal>. And then you have to implement the compareTo(Animal other) method that way you like it.

@Override
public int compareTo(Animal other) {
    return Integer.compare(this.year_discovered, other.year_discovered);
}

Using this implementation of compareTo, animals with a higher year_discovered will get ordered higher. I hope you get the idea of Comparable and compareTo with this example.

Your comparable class should be whatever you're sorting. In this case you're generating a random array of int, so you don't actually need to implement compareTo, because Integer has already implemented compareTo. You would create a new class width if the things you were sorting were more complicated than integers.

For example, if your Applet had a bunch of circles it was going to sort by size, you would have something like:

public class Circle implements Comparable<Circle> {
    private Point center;
    private double radius;

    public Circle(double radius, Point center) {
        this.center = center;
        this.radius = radius;
    }

    // Other drawing functionality

    public int compareTo(Circle c) {
        if (c.radius > radius) return -1;
        if (c.radius == radius) return 0;
        return 1;
    }
}

You see? Our object is more complicated, so we need to teach Java how to compare one circle to another, because it doesn't know.