A point is a section of glass tube with one or both ends stretched long and thin so as to make a good handle for various lamp working activities. The term is somewhat confusing as it may be used to refer to a portion of tube as described above, but also may refer only to the stretched section. A point is triply useful; the length keeps your hands away from the flame, the small diameter gives you the ability to rotate a larger attached piece quickly, and the (small) wall thickness allows it to cool off quickly if you accidentally heat it up.

The process of point creation is known as pulling a point, and is a very good place to begin a study of lamp working. Standard pyrex tubing comes in 3-foot section which are much too unwieldy to use by themselves. One technique is to pull several points to break the tube down into manageable sections. Alternatively the tube can be melted apart without pulling a point, and a blow tube attached, but points are often more convenient. The timing varies depending on the dimensions of tube you are using (I recommend 5/8" heavy wall to start), but the steps remain the same:

Heat a section of tube.
Heating a section of tube involves smooth rotation (as does everything in glass blowing) to heat evenly. Depending on how long and thick you want the point and the size of your tube and torch you may need to actually gather some glass together or stretch slightly as you are heating. The important thing is getting even heating throughout the glass you want to stretch.
Remove the glass from the flame and continue rotating.
Before you actually pull the point you must wait until you have the right heat distribution in the glass. While waiting you must keep the hot glass on center so it doesn't droop down, alternatively you can move the tube into a vertical position so the drooping occurs on the axis of rotation, but don't use that as a crutch.
Pull the point.
Pull slowly at first until the glass is of even thickness, and starting to lose it's orange glow, then pull quickly to extend the length of the point as far as possible. If you pull too soon the hot glass will stretch to a very narrow diameter, be of uneven thickness, or just plain bent. If you wait too long you won't be able to get the length you need before the glass freezes.
Hold it tight.
At the point when the glass freezes you should be pulling tightly. Assuming the thickness is even this will ensure that the point is straight. Even if your point is horribly off-center (quite likely in the beginning), if the main length of it is straight you will be able to recenter it by heating at the point where it connects to the thicker tube. On the other hand, if the thin part itself is not straight there is nothing that can be done.

Pulling points is a fundamental building block of lamp working, and will teach you many many things about glass and principles of thermodynamics. The kind of points you pull really depend on the application, but since they are throw-away parts they do not generally need to be of high quality. Experienced blowers can pull several points in rapid succession from the same tube. They will be thrown away after use, so they are the perfect excercise for the beginning apprentice.