The way that I remember being told about the Chabad Rebbe of blessed memory is that davening and/or talking/writing to him is like confiding in your lawyer who has a very strong relationship with the judge.
Since the Rebbe is so close to Hashem, he can petition for you and do things for you that your direct plea to the judge wouldn’t accomplish. The answer’s not always Yes or in your favor, but the Rebbe has more pull and in general gets better results for his clients.