Непонятен смысл 'throws'

public class Off {
    public static int area(int width, int height) {
    if (width < 0 || height < 0) {
        throw new IllegalArgumentException("Negative sizes: w = " + width + ", h = " + height);
    }
    return width * height;
    }
    public static void main(String[] args) {
        int s = area(-1, 2);
    }
}

public class Off {
    public static int area(int width, int height) {
    if (width < 0 || height < 0) {
        throw new IllegalArgumentException("Negative sizes: w = " + width + ", h = " + height);
    }
    return width * height;
    }
    public static void main(String[] args) throws IllegalArgumentException {
        int s = area(-1, 2);
    }
}

throw new IllegalArgumentException("Negative sizes: w = " + width + ", h = " + height);

throw new Exception("Negative sizes: w = " + width + ", h = " + height);

public class CB {
    public static int area(int width, int height) throws Exception {
    if (width < 0 || height < 0) {
        throw new Exception("Negative sizes: w = " + width + ", h = " + height);
    }
    return width * height;
    }
    public static void main(String[] args) throws Exception {
        int s = area(-1, 2);
    }
}