What is the idea of verify in mockito and when should I use it

I understand that Mockito.verify() is used to ensure that a mock method is being called with required arguments. But I don't understand the intention of this. I often see tests similar to this:

public class UserDAO {
    public long create(User user) {
        //...
    }
}

public class UserService {
    private UserDAO userDAO;

    public UserService(UserDAO userDAO) {
        this.userDAO = userDAO;
    }

    public long createUser(User user) {
        return userDAO.create(user);
    }
}

public class UserServiceTest {
    @Test
    public void testCreateUser() {
        UserDAO userDAO = mock(UserDAO.class);
        when(userDAO.create(any(User.class))).thenReturn(anyLong());

        UserService = new UserService(userDAO);
        User user = new User("John Smith");
        userService.createUser(user);

        verify(userDAO).create(user);
    }
}

Test verifies that create method of UserDAO is invoked when createUser method of UserService is invoked. It looks absurd. If I change the implementation of UserService in such way that it doesn't invoke method of UserDAO my test will fail even if the implementation is correct.

I admit that there might be cases when it's necessary to verify that method is invoked exact number of times but such cases are infrequent.

Most likely I don't understand the idea of verify and it's not a mockito-specific feature. Could you explain it in simple words and when it really makes sense to use it.