as I understood, the method clone() gives us the ability to copy object (no refernce) in Java. But I also read, that the copy is shallow. So what the point? Which ability the clone() method gives me, that a simple assingment doesn't?
The difference is that you can modify the cloned object without modifying the original object.
Point p = new Point(1,2);
Point p2 = p.clone();
Point p3 = p;
p2.x = 5;
p3.y = 7;
The change on p3 does feed back to p, while the change on p2 does not.
Let's see how the situation is after the individual statements (assuming 1, 2, 5, 7 would be objects):
Point p = new Point(1,2);
            .-----.    .-----.
 p  ----->  |  x -+--> |  1  |
            |     |    '-----'
            |     |    .-----.
            |  y -+--> |  2  |
            '-----'    '-----'
Point p2 = p.clone();
            .-----.    .-----.    .-----.
 p  ----->  |  x -+--> |  1  | <--+- x  |  <----- p2
            |     |    '-----'    |     |
            |     |    .-----.    |     |
            |  y -+--> |  2  | <--+- y  |
            '-----'    '-----'    '-----'
Point p3 = p;
            .-----.    .-----.    .-----.
 p  ----->  |  x -+--> |  1  | <--+- x  |  <----- p2
            |     |    '-----'    |     |
            |     |    .-----.    |     |
 p3 ----->  |  y -+--> |  2  | <--+- y  |
            '-----'    '-----'    '-----'
p2.x = 5;
            .-----.    .-----.    .-----.    .-----.
 p  ----->  |  x -+--> |  1  |    |  x -+--> |  5  |
            |     |    '-----'    |     |    '-----'
            |     |    .-----.    |     |
 p3 ----->  |  y -+--> |  2  | <--+- y  |  <----- p2
            '-----'    '-----'    '-----'
p3.y = 7;
            .-----.    .-----.    .-----.    .-----.
 p  ----->  |  x -+--> |  1  |    |  x -+--> |  5  |
            |     |    '-----'    |     |    '-----'
            |     |    .-----.    |     |
 p3 ----->  |  y  |    |  2  | <--+- y  |  <----- p2
            '--+--'    '-----'    '-----'
               |     .-----.
               '---> |  7  |
                     '-----'
                        An assignment copies the reference of an instance to a variable. A clone operation will clone the instance (and assign a reference to the clone).
With assignment, you'll end up with multiple variables pointing to one object, with cloning you'll have multiple variables that hold references of multiple objects.
SomeCloneable a = new SomeCloneable();
SomeCloneable b = a;                     // a and b point to the same object
/* versus */
SomeCloneable a = new SomeCloneable();
SomeCloneable b = a.clone();             // a and b point to the different objects
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