-Why is it a good practice?
Because you can pass the class around and be sure it will never be modified by a "rogue" code. Same for Java Strings, they're immutable.
-Could you name a situation where this approach can be used?
It's very useful on big projects where many teams work together, or when designing a framework or an API. In these situations, since you're not responsible of parts of the code, you can never trust that an object you pass to other parts of the code won't be altered. Use immutability if you need to ensure the object won't be modified.
-What about constants or read only variables? Is not that very similar?
Not in Java because we have neither const nor read-only. All we have is the final keyword that ensures an object reference won't be modified beyond first assignment. But the underlying object can still be modified even if the reference can not. Immutable classes ensure an object state won't be altered after creation.
-In the article says, that this is not good for the performance of the application. But why?
Because every time you need to modify the object, you need to create new instances. Same for Strings, you can't do myString.append("42"), you need to do myString = myString+"42", which creates a new String object.
