The sages say that Jerusalem will expand and fill the entire land of Israel. What does this statement mean?
In the future time, the holiness of Jerusalem will spread throughout the entire land of Israel.
The wording of our sages is as follows: "In the future, Jerusalem will be like all of Israel, and Israel will be the entire world."
The second part of the statement can be explained according to the halachic rule, that any part of Israel conquered in accordance with Jewish law takes on the holiness of Israel, with all the incumbent rules. When Moshiach comes, the entire world will take on the holiness of Israel, and all the agricultural laws that are currently applicable only in Israel will apply throughout the world.
Chassidic teachings explain that the Creator provides a flow of G-dly light and energy to the whole world. However, in most of the world this light must pass through "shields" to reduce its intensity, so that the world is able to contain it. The Land of Israel, on the other hand, is able to withstand a greater force of G-dliness, and the G-dly light that reaches passes through fewer spiritual barriers.
In the future, the entire world will be elevated, and the level of G-dliness that is now found only in Israel will spread through the entire world. Therefore, all the mitzvot that apply now only in Israel will apply in every place.
In addition to the elevation of the whole world, the Land of Israel will also be elevated. This is the meaning of the first part of the statement of our sages: "Jerusalem will be like all of Israel." Today, Jerusalem has a special level of holiness; in the future, that holiness will expand to the entire Land of Israel.
This process of elevation will come as a result of studying Torah and fulfilling mitzvot in every place in which we find ourselves. The Torah and mitzvot add holiness to the world, which will be revealed with the coming of Moshiach.
(Devarim 11:24. Yalkut Shimoni, Yeshaya, 503. Likutei Torah Admur Hazaken, Masei, 87:2. Torat Menachem 5751, vol. IV, p. 60)