A stiff shaft is firmer and harder to bend than a regular shaft. That said, flexing a stiff shaft is not as simple as just swinging harder. The more club-head speed you generate, the stiffer the shafts on your clubs should be. A quick, athletic swing can generate club-head speed, but a long, slow, accelerating arc can generate more. When your swing is matched with the correct shaft flex, it can help you maximize distance and control on all of your shots.
Material and Torque
Most golf shafts are made of either steel or graphite. Steel is the traditional material and is still used in many irons. Graphite is used in almost all drivers produced today and is available in most other clubs; the term describes any number of composite materials.
Club makers strive to produce low-torque shafts. Flex is the bend a shaft experiences from grip to club head during your swing. Torque is the amount of twist the shaft allows when you hit the ball on the heel or toe of the club. That twisting can help correct for off-center strikes if the shaft's elasticity is such that it twists back to center during your swing. It can also make a shot worse if it does not twist back.
Club makers use the term "kick point" quite a bit when discussing and selling shafts. The kick point is where the shaft flexes the most. A club with a high kick point will produce a lower trajectory; a shaft with a low kick point will launch the ball higher into the air. Stiffer shafts are usually higher kick-point clubs.
A faster swing requires a stiffer shaft or exquisite timing. You can get your swing speed measured on a launch monitor, or you can visit your local shop or range and hit a variety of clubs with different flexes. Either way, you'll see immediately what type of shaft is best for you. If you swing in the 90 mph or faster range, a stiff shaft will probably help you. If you are in the 80 mph or less range, the regular shaft is clearly your choice. At that speed, you won't be able to flex the shaft properly and you will likely never be able to correct a high slice.
Golfers with slower swings will likely never see an advantage to hitting a stiff-shafted club. On the other hand, golfers with faster swing speeds can still play a regular-flex club with some dexterity. In that situation, it is all about the rhythm of your swing. Sometimes, a player with a 90 mph swing speed will find he hits the ball farther with a weaker shaft. He will give up a bit of control for that extra snap in the shaft, however.