Thrown olives are stuffed olives which are dropped into a jar by a machine as they are packed, rather than being carefully placed by hand. While this distinction might seem petty, some people are willing to pay more for placed olives, olives which are carefully oriented in the jar so that their stuffing faces out, creating a more even, attractive look in the jar. Ultimately there is no difference in flavor between the two, although placed olives tend to be more expensive because of the manual labor involved.
Generally, the term “thrown olives” is only used in reference to stuffed olives, because most consumers don't care which direction unstuffed olives are facing. Many Mediterranean nations have a long tradition of stuffed olive production; olives can be stuffed with things like nuts, pimentos, anchovies, onions, and other pickled fruits or vegetables. These olives can be used in cocktails, on salads, and in ornamental olive plates, and they are quite popular in some regions.
When stuffed olives are made, they are pitted and the stuffing is inserted into the hole left behind after the removal of the pit. This is typically accomplished by machine in modern olive processing facilities, although a few communities continue to produce hand-stuffed olives for commercial sale. Then the olives are packed in brine, salt, or oil for curing. After the olives are cured, they can be packaged for sale. Typically stuffed olives are packed in cans or jars which are tightly sealed to prevent the intrusion of unwanted bacteria.
Obviously, the contents of a can of olive are not visible until the can is opened, and therefore the placement of the olives is not very important. However, olives in a jar are visible, and some people use olive jars decoratively, or they at least like their olives to look attractive until the jar is opened. This is why some producers distinguish between placed and thrown olives, offering placed olives for a slightly higher price. Since the stuffing is usually tightly inserted into the olives, you don't need to worry about thrown olives losing their filling as a result of being haphazardly tossed in, although there might be slightly fewer olives per jar when a human doesn't physically pack them as neatly and tightly as possible.
Once a jar or can of olives has been opened, the olives will need to be refrigerated. Canned olives should be transferred to another container as acids can sometimes eat at the can, potentially causing it to fail or contaminate the food. Olives in a jar can be stored in the jar until they have been consumed. Whether thrown or placed, the arrangement of the olives will generally become random once the jar has been opened and handled. Most markets carry jars of olives; the next time you're in the store, you can check for thrown olives in the olive section.