We do not pray to God through angels or other intermediaries from the upper worlds; instead, we pray directly to God. Nevertheless, it is permissible to request that the righteous pray on our behalf. This does not raise a concern about people praying to the righteous person himself, for he is only human and it is clear to all that he is not the source of anything good or bad.

It is permissible to request that the righteous pray on our behalf:

It is prohibited to pray to angels or other higher spiritual powers to act as intermediaries between us and our Creator. But there is no prohibition [to request that] the righteous – whose prayers are fitting to be answered – [pray on our behalf, for they] are creatures of this lower world.

The righteous are human beings, so there is no danger that people will serve them as opposed to God:

There are two reasons for this: One is that because of the high level of that middle world [of the angels and other purely spiritual beings] people are liable to mistakenly worship them through praying to them to be intermediaries. People will then come to think that the angels can cause good or harm and that it is appropriate to pray to them as independent entities. But it is impossible for them to make such a mistake with regard to creatures of this low world…. A second reason is that the lofty heavenly beings are not subject to occurrences and shortcomings of this world…. Therefore, if people pray to them, they will mistakenly think that, just as the [higher beings] are not subject to chance and weakness, so too, they have the ability to fulfill everyone’s wishes and save people from random accidents and problems. But human beings, as righteous as they are, are subject to the misfortunes of this world and its occurrences. Therefore, when people come to the righteous and ask them to pray on their behalf, there is no concern that those people will make the mistake [of thinking the righteous have independent powers], since the same unfortunate event that happened to them can also happen to the righteous person. (Rabbi Moshe of Trani (Mabit), Bet Elohim, Sha’ar HaTefilla 12)

A Torah sage who prays for another person does not approach his prayer as an outsider, for he feels the other’s pain as if it were his own. He is not simply like an independent agent or a separate person serving as a go-between, but he prays, in a broad sense, for himself. There is actually an advantage to the righteous man’s prayer. Because he is considered like the “head” of the Jewish people, it is natural that he should be the one to stand before God.

All of Israel are partners, as one body with one soul, and when one is in pain, another feels it and shares his pain. This is the source of Rava’s statement: “One who prays for another must make himself ill on his behalf” (Berakhot 12b). The explanation is as follows: He should realize that he himself is sick [because all of Israel is as one body and soul]. Since both of them are in pain, it is better that the head should enter [before God to pray] rather than, for instance, the foot. The Torah scholar is the head, and the one [originally] in pain, who is now experiencing divine judgment and is being somewhat rebuked by Heaven, is like the foot. [Since that is the case,] it is better that the “head” enter [before God instead of the “foot”], since both are the relevant parties [who need to pray] and the Torah scholar is not merely a negotiator on behalf of another. (Rabbi Moshe Sofer, She’elot UTeshuvot Ĥatam Sofer, Oraĥ Ĥayyim 166)

Any physical deficiency or need a person has is the result of some spiritual deficiency within him. The connection between the tzadik (righteous person) and the sick person that takes place when the tzadik prays on his behalf enables the sick person to repair his sin. It naturally follows that the need for punishment is removed and the sick person is able to recover.

We need to understand [the mechanism of how] a tzadik prays and his prayer is answered. This seems like a change [in the divine plan], yet God, in His ultimate Oneness, cannot change, heaven forbid. The matter can be explained as follows: When a tzadik prays for a person he does it with all of his 248 limbs and 365 sinews, without any external thoughts, and he connects the person he is praying for with his own 248 limbs, thereby elevating him. That is why he is answered. For where does the original deficiency come from? Certainly it is a punishment for a sin [the sick person] did with one of the limbs of his body. When the tzadik enwraps and covers him [through prayer], the limbs of the sick person become one with those of the tzadik, and that naturally repairs his sin. Once the sin is repaired, the punishment passes and leaves him. (Rabbi Elimelekh of Lizhensk, Noam Elimelekh, Parashat Emor, “Eleh Mo’adei Hashem”)