To meet the expectations of their customers, a 'jury' is how a promoter selects the art/craft combination that will be exhibited at their show.
A 'juried' art and/or crafts show means that the artist or crafter must submit certain materials to the show committee, while applying to participate in the show. The requested materials can be any combination of: a specified number of slides, photos or electronic images of their work with definitions; an artist's statement; a description of how the artist executes their art form and what materials the artists uses in said work; a link to your website; a photo or two of your booth set-up; a specified list of the items you wish to sell at that show; and often a nonrefundable fee to have your work 'juried'. (Rarely, certain arenas may even request a physical sample).
All of the requested information is then presented by the show's promoter to their panel of judges (a committee of experts) who decide which applicants meet the promoter's criteria for that particular show. Jury standards and fees can vary quite a bit, from show to show.
Juried shows often have a higher booth fee, but in my personal opinion they are worth every dime. Many juried shows charge an entry fee to their customers, and if someone is willing to pay to get into a show to purchase, they are serious about what they are looking for and they know they will find quality products. Juried shows also weed out a lot of 'buy-sell' vendors (note I said 'most,' not all, because some folks are just unscrupulous!). The promoters of most juried shows also take better care of their vendors, do quite of bit of advertising for their show, and usually have on-site officers to help with crowd control and eliminate theft. Because they have specially selected their group of artists, they usually limit the number of 'same products' and often offer cash awards for a list of contests you can enter with your works.
Answer contributed by Dale "Cougar" Armstrong