The actual balloon is referred to as The Envelope, which is constructed from long nylon sections called gores. The gores extend from the base of the envelope to the crown and are made up of many smaller panels. The main part of the envelope (the bottom two thirds) is normally made from a combination of nylon or polyester, the same type of material that parachutes are made of. It is very tightly woven and is coated with a material that makes it extremely air tight and durable. Nylon works very well in balloons because it is lightweight, but it is also fairly sturdy and has a high melting temperature.
The bottom part of the envelope, referred to as the skirt (nearest to the burner) is made from a material called Nomex. Nomex is an industry standard flame resistant material used in other industries such as Formula 1 Racing and also in the suits of Firefighters. It is used near the mouth (base) of the envelope as this is area prone to the most heat from the burner.
The material used nearer the top of the envelope is known as Hyperlast. It has been around for many years and is generally used in the top 3rd of the envelope. What makes Hyperlast desirable to use is that the nylon base fabric is woven from a heavier yarn, which increases the strength a great deal. Also Hyperlast has a silicone coating added to both sides of the fabric which helps to protect the envelope from the growth of mould or fungi.
Envelopes come in many different shapes and sizes, depending on what the balloon will be used for. You can view the many different types of envelope offered by Lindstrand Balloons on their website, one of the most established UK manufacturers of all balloon products.