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On a bicycle, the stem is the piece connecting the handlebar to the steerer tube of the fork. There are two different types of stems, corresponding to the two types of headset: threaded headsets and threadless headsets.

For a threaded headset, the stem is an upside-down "L" shaped piece of metal. The downward pointing piece is inserted into the steerer tube and is held there by a wedge-shaped quill that is pulled up tight using a long bolt running the length of the stem. The other section of the stem points forward and attaches to the handlebar via some sort of a clamp. The exact angle of the stem varies between bicycles. On most road bikes, the stem will angle down; the point of attachment for the handlebar is actually below the bend in the stem. Stems for mountain bikes, however, generally angle up a fair bit.
The height of this type of stem can be easily adjusted. Simply loosen the bolt on top of it which runs into the steerer tube, and give it a tap with a hammer. This dislodges the quill inside the steerer tube. Then adjust the height, and after making sure it is centered over front wheel, retighten the bolt. The bolt should be relatively snug, but take care not to overtighten it, as this will only damage the inside of the steerer tube.

Stems for threadless headsets are a much more simple design. On this type of a headset, the steerer tube actuall protrudes above the head tube of the bike. The stem is essentially a piece of tubing with clamps at both ends. One clamp attaches to this piece of the steerer tube, the other to the handlebar. The stem is actually responsible for holding the fork in the bike. This can be a much more sturdy design, and is used on most mountain bikes. Very little changes can be made to the height of this type of stem, however. At best, one can place a few spacers between the stem and the headset, raising it slightly.

Angle and length of the stem are one of many factors that significantly influence the ride of a bike. Longer stems with a very shallow angle will put the rider further forward over the bike. This is very good for aerodynamics and hill climbing. An extreme form of this is seen on road bikes. Shorter, steeper stems, especially when coupled with a riser bar, will make for a tighter cockpit on a mountain bike, increasing mobility. This is very handy on more technical trails.