On Lag BaOmer of a Shemitah year, at some point between the customary bonfire and the haircuts, some knowledgeable people will get up and declare ownerless the etrog jelly that they made after Sukkot. A short while later, they will reclaim their food. Before Shavuot, they will declare ownerless the olives they picked, and then reclaim them. Earlier, before Pesach, they will do the same thing with the wine that was produced through Otzar Beit Din. The pattern is repeated through Shemitah with many types of fruit.
These actions are indirectly derived from the verse, “And your cattle and the [wild] beasts in your land may eat all its yield” (Vayikra 25:7). Why is it necessary to specify “the cattle” (i.e., domesticated animals), when the verse also mentions “the beasts in your land”? For if a wild beast may eat of the Shemitah produce, a domesticated animal certainly may!
Our Sages use this verse as grounds for the following exposition: “Once the fruits have disappeared from the field and are unavailable for wild beasts, the fruits must disappear from the home as well and be unavailable for domestic animals.” In other words, once there are no more fruits on the tree because they have all either fallen off or rotted, people may no longer hold onto them at home either. Rather, they must dispose of them. This disposal is called biur.
It would seem that this biur should be similar to biur chametz, which involves burning the forbidden food. Indeed, there are some who require this (Rambam, for example). However, the generally accepted practice is to remove the fruit from the home and declare them ownerless. After this has been done, it is permissible for the former owner to reclaim them. In theory, of course, someone else could come along in the meantime and acquire the food that had been declared ownerless. Nevertheless, it is rare to find people trying to find a bargain this way. This is likely because those who declare the items ownerless can do so in front of three good friends, and rely on their not taking advantage of the opportunity to acquire the items for themselves.
The times mentioned above for declaring certain produce ownerless (before Pesach, on Lag BaOmer, and before Shavuot) were designated by the Sages, based on their estimates when each type was no longer available in the fields for the wild beasts. They designated other times for other fruits. Today, various organizations (such as Machon HaTorah VeHa’aretz) produce Shemitah calendars which detail the specific dates relevant to many different fruits and vegetables.