Just like Jews must rest every seventh day, the land of Israel must “rest” every seventh year. We call this year “Shemittah,” meaning that we leave the land alone. Instead of working it, we withdraw from it, leaving whatever grows to be free for all. (The verse continues that the needy and even animals of the field can eat freely from it.) Accordingly, one may not lock up his field or gather in his produce.
The reason for this mitzvah is similar to underlying rationale of Shabbos: we step back in recognition that God is the One Who created the world and He’s the One running the show. Similarly, He is the “landlord.” The land belongs to Him, so sometimes we have to step back and leave things in His control. This refocuses us so that we recognize that we’re not the ones who cause wheat, barley, olives and grapes to grow; He is. By stepping back and leaving things in God’s metaphorical “hands,” we learn to place our trust in Him. (A fringe benefit is that opening our fields to the public helps us to cultivate the trait of generosity.)
There is a halacha l’Moshe miSinai (an unrecorded law given to Moses at Mt. Sinai and transmitted orally) that the obligation to back off from the land actually begins 30 days before the Sabbatical year. (See Talmud Moed Katan 3b.) This mitzvah is connected with #112 (in parshas Ki Sisa), the obligation to refrain from plowing and harvesting during Shemittah.
This mitzvah applies to both men and women, but only in Israel (see Leviticus 25:2, “When you enter the land…”). There are Rabbinic applications of Shemittah to territories not part of Israel proper that were captured in the time of King David. (See Talmud Gittin 8b for the status of Syria, the prototypical example of such conquered territories.) This mitzvah is the topic of the entire tractate of Sheviis, which has no gemara in the Babylonian Talmud. (With the exception of tractate Brachos, the agricultural order of Zeraim has no gemara in the Babylonian Talmud, as those laws were inapplicable outside of Israel. The Jerusalem Talmud, composed in Israel, is another story.)
This mitzvah is codified in the Mishneh Torah in Hilchos Shemittah. It is #134 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #20 of the 26 mitzvos that can only be performed in Israel according to the Steipler Gaon.