Are you asking why checkDay() is a private method? It checks that you've given the constructor a valid day of the month and prints out an error message if you haven't. Nothing is supposed to call that method from outside the class, so they made it private.
First want apologize for not informing clearly into doubt.
The question this in that code, see:
Note: I am Brazilian! I am learning English.
Sorry by disorder!
I know declaration variable string, int and derivates. But, in that case, no this declaration the variable birthDate how String ou int.
The variable this declared how Date. By which reason ?
Note: I no using the class Date of Java (import java.util.Date).