A leaflet fills a role halfway between a booklet and a flyer. Where a flyer is a single piece of unfolded paper, and a booklet is a small collection of pages usually bound or stapled together, a leaflet is a single piece of paper that is folded to approximate pages without requiring any form of stitching or binding. Typically a leaflet will be made from a page of A4 or 8½ x 11 paper folded accordion-style between one and four times. Often they will be printed on both sides to maximize available space. There are no set rules, however, and they may be made of any size paper and folded any way the publisher feels would best present the information.
Leaflets are extremely cheap to produce and easy to carry around, and are often distributed as advertising or propaganda. The front fold of a leaflet will often carry an eye-catching picture and a bold headline that sums up the message of the leaflet, and each additional fold contains more detailed information about a specific point or part of the message. The idea is that the front fold will interest the target enough to read the rest of the leaflet.
In museums, aquariums, art galleries, and other such buildings, leaflets are often available to help guide guests to the various exhibits and help them find displays that would be of interest to them. Often an entire side of the leaflet is devoted to a map of the building. Usually printed on high quality glossy paper with full color illustrations, these are available free at information desks or the ticket booth. Leaflets folded three to four times fit most conveniently in a pocket for when it is not needed.
At protest rallies or other such mass gatherings, leaflets are extremely cheap ways of distributing the propaganda around the crowd. In this case, the leaflet will often be printed on plain colored paper, usually orange or yellow, and produced as cheaply as possible, usually with a photocopier and hand folded by volunteers.
Support group meetings use them to provide further information about the group's activities and mission. Doctor's offices use them to distribute information about various diseases and health risks. Stores often put them in displays for advertising purposes. The phone company, cable company, or any of various utility companies may include leaflets with your monthly bill to inform you of other services you might want to take advantage of. The list goes on and on. Any time a person or organization wants to distribute more information than a flyer is designed for but doesn't want to incur the additional binding expense of a booklet, a leaflet is the perfect middle ground.