The Sefer HaChinuch gave a few reasons for the mitzva of shmita (mitzva 84), these are his golden words:
A. One of the roots of the mitzva is to instill the concept of the renewal of the world in our hearts and to draw a strong picture of this concept in our minds. G-d created the heavens and the earth in six days and, on the seventh day, when He refrained from creating, he caused Himself to rest. And in order to uproot the idea of the world coming into being on its own (the opposite of creationism), which the atheists use to destroy the Torah and break down its walls- we are commanded to make a daily and yearly count of six years and to rest on the seventh. This will ensure that this concept will remain forever etched in our minds, which is similar to the way that we have six work days and one day of rest. This is why the Holy One Blessed Be He commanded us to render all the crops that grow during that year ownerless [hefker], aside from not working the land, so that we would recall that the land which grows the fruits each year does not do so of its own power, but rather that it has a Master. And when He so desires, He commands that the produce be rendered ownerless (hefker).
B. There is another benefit- to acquire the trait of benevolence, because there’s no one more generous than one who gives without expecting anything in return.
3. Yet another benefit exists here, that one should increase his faith in G-d, Blessed be He, because all who are able to control their hearts to give and to render all their produce and their land ownerless (hefker) for an entire year, and who he and his family do so their entire lives, will never become overly greedy and will never be overcome by a lack of faith.
Even the Rambam in his book Moreh Nevuchim (chelek 3 39), gave a reason for the two mitzvot of shmita. Here is what he wrote: “The entire mitzva of shmita is saturated with compassion and clemency for all people, as it is written, “And the destitute of your nation shall eat, and the animal of the field shall eat the remainder”. Another reason for shmita is so that the yield will increase because the soil will become strengthened during the year that it rests.