The edges of the inside of a pool table are called rails. Ranging from about 2.5 to 3.5 inches (6.35 cm to 8.89 cm) in width, the rails are normally made of the two pieces. The top part is made of the same hardwood or other material as the rest of the table.
The cushion is a long, wedge-shaped piece of hard rubber that is glued to the side of the rail that faces into the table's playing surface. Cushions are covered with the same felt cloth used to cover the slate and should provide a consistent response to any ball that strikes them. Cushions are made of hard rubber, and are glued to the rail. Canvas is then glued to the rubber to keep it from bouncing more than once when a ball strikes the cushion.
The final piece of the table is the cloth. Pool tables normally use a tightly-woven cloth made primarily of wool along with a synthetic such as nylon added for more durability. The cloth provides a consistent and smooth playing surface.
Billiard cloth is often referred to as felt, but it actually is nothing close to being like real felt. Real felt is not a woven material but is formed from compressed and matted fibers and would not work well at all as a smooth playing surface.
Sources:
http://entertainment.howstuffworks.com/billiard-table.htm
http://en.wikipedia.org/wiki/Billiards_table