The verse "He shall rule from sea to sea, and from the river to the ends of the earth" is explained by Rashi in our parsha as referring to King Moshiach. This is the intention in Balaam's prophecy "and he shall rule from Jacob" — "and there will be another ruler after Jacob... and this refers to King Moshiach, as it is said about him, 'He shall rule from sea to sea.'" We also find this expression in the prophecy of Zechariah, which explicitly speaks about King Moshiach — "Behold, your king will come... humble and riding on a donkey... and his dominion shall be from sea to sea, and from the river to the ends of the earth." This is also brought by the Rambam in his explanation of the verse (in Balaam's prophecy) "and he shall uproot all the sons of Seth" — "this is King Moshiach, as it is said about him, 'and his dominion shall be from sea to sea.'
Simply put, the intention is that King Moshiach will rule and have dominion over the entire world, as explained by the Ibn Ezra: "from the southern sea called the Red Sea to the northern sea, which is the Ocean, and from the river that flows from Eden, which is at the beginning of the east, to the ends of the earth, which is at the end of the west."
It requires explanation why it is stated "from sea to sea, and from the river to the ends of the earth" instead of simply saying "over the entire earth" or something similar. Additionally, why mention the seas ("from sea to sea") when the kingdom of Moshiach is over the lands (the inhabitants of the world)?
This can be explained according to Chassidus based on the words of the Alter Rebbe, that the completeness of the days of Moshiach depends on "our actions and service throughout the duration of the exile," that through the study of Torah and the fulfillment of mitzvos — "if you will listen to His voice" — we prepare the entire world, and the Jewish people in particular, for the ultimate perfection of the days of Moshiach. Since the measure of the Holy One, blessed be He, is "measure for measure," it is understood that "our actions and service" that bring about the coming of Moshiach must be similar to the elevations that will be then. This means that in order to reach the revelation of the kingdom of King Moshiach, which will be "from sea to sea, and from the river to the ends of the earth," there must be a personal service of each individual akin to this.
This is further clarified by what is explained in the book Maor Einayim (by the holy Rabbi from Chernobyl) in the name of the Baal Shem Tov, "that every Jew must rectify and prepare the part of the stature of Moshiach that pertains to his soul" [as explained elsewhere, the hint to this in the revealed Torah — that in the Jerusalem Talmud they expounded the verse "a star shall go forth from Jacob" on every Jew, and elsewhere in the Jerusalem Talmud (and also in several Torah commentators) they expounded it on Moshiach, meaning that in every individual there is a "part of the stature of Moshiach"], and it is also explained in the Tanya, that the revelation of the innermost point in the heart of every Jew, which is his connection to the Holy One, blessed be He, beyond human understanding ("beyond reason"), is akin to "the exodus of the general Shechinah from exile and captivity forever and ever."
Accordingly, it can be said that this is the precision in the wording of the verse "He shall rule [and his dominion shall be] from sea to sea, and from the river to the ends of the earth," because in order to merit the complete revelation of the kingdom of King Moshiach throughout the entire world (a general redemption), there must be something similar in the service of man (a personal redemption), where the spark of Moshiach within each individual (the innermost point in the heart) must rule and have dominion over all parts and matters of the person. Since the main matters of a person are divided into "from sea to sea, and from the river to the ends of the earth," therefore it is also stated so regarding the kingdom of Moshiach.
To explain the matter:
The difference between "sea" and "land" is that "sea" indicates hidden things (like the creatures of the sea that are concealed by the sea's waters), and "land" indicates revealed things. In the service of man: "sea" refers to the powers of the soul within the person himself, and "land" — his actions in the world outside of him.
Now, regarding "sea," the verse emphasizes "from sea to sea," indicating that there are two "seas" over which there must be dominion and rule. The nature of these two "seas" in the service of man can be explained based on what is written in the prophecy of Zechariah: "And it shall be on that day that living waters shall go out from Jerusalem, half of them to the eastern sea and half of them to the western sea," from which it can be understood that the two "seas" mentioned regarding Moshiach — "from sea to sea" — are "the eastern sea" and "the western sea," the beginning of all seas and their end.
In the service of man: "The eastern sea" represents the beginning of all powers, which is the power of wisdom (the beginning of intellect), and "the western sea" is the end of all powers, which is the power of action. A person's service is not complete until he rules and has dominion from the beginning of his powers, the power of wisdom, to the end of his powers, the power of action.
This means: At the outset, a person must have dominion over his power of wisdom (and intellect), ensuring it is entirely in holiness, because the overall conduct of a person, in all its details, depends on the intellect in the head, which governs the heart to guard it from evil desires, etc.
However, on the other hand, there must be effort and endeavor to have dominion until the "western sea," his power of action. As we see in reality, a person may understand well in his intellect how his conduct should be in all details, but he lacks the power to control himself to bring it into action, and even into actual deed. It is possible for him to have a good feeling for everything holy, including good thoughts and even good speech, yet it does not come to actual deed — and the deed is the main thing.
This is the emphasis that a person's service must be "from sea to sea" — for his service cannot be complete without dominion and rule over these two extremes, "the eastern sea" and "the western sea," wisdom and action.
However, all this pertains to the person himself. Even his power of action, actual deed, which is only in matters outside of him, can still be part of his service with himself, where the test that he is entirely permeated with holiness is when it also comes to actual deed.
This is why the verse continues that it is not enough "from sea to sea," but there must also be dominion "and from the river to the ends of the earth."
The matter is as follows:
As mentioned above, the explanation of the Ra'avad is that "the river" is the "river that goes out from Eden," whose purpose in going out from "Eden" is (as the continuation of the verse states) "to water the garden," which at the beginning of creation was the place of Adam HaRishon, "and He placed him in the Garden of Eden to work it and to guard it." In general, this refers to the entire world, which is called "My garden" — the garden of the Holy One, blessed be He — as it is written, "I have come to My garden, My sister, My bride." This is the service of man, "to work it and to guard it," that through his service in refining and purifying the world, he acts and reveals throughout the entire world that it is recognizable as "the garden" of the Holy One, blessed be He.
This is the emphasis of the verse "and from the river to the ends of the earth" — that a person must not close himself within his four cubits and not think about the world around him, saying "I have saved my soul," while he is in "Eden" (a place of G‑dly revelation) — rather, he must engage in the work with the "river," "to water the garden," to refine and purify (with the power of the "river" that goes out from "Eden") the entire world, "to the ends of the earth."
This work is what brings about the perfection of the kingdom of Moshiach, "and he shall have dominion from sea to sea and from the river to the ends of the earth," which, in addition to the perfection of Moshiach himself, "My servant shall prosper, he shall be exalted and lifted up, and shall be very high," he will "rectify the entire world to serve G‑d together, as it is said, 'For then I will turn to the peoples a pure language, that they may all call upon the name of the L‑rd,'" in the true and complete redemption, immediately and without delay.
"(From the talk of the 12th of Tammuz, 5733)"