Glucose is one of the "simple sugars" -- an ironic name, because the chemistry of these compounds is rather complex. The naming system for sugars reflects this complexity. Chemists use prefixes like alpha and beta to denote different versions of glucose and other sugar molecules. To the uninitiated, these prefixes may seem mysterious, but once you understand sugar structure, their nature and purpose will become clearer.
Linear and Cyclic
Each molecule of glucose has a carbon backbone with -OH groups and hydrogen atoms attached to it. At the top of the chain, an oxygen atom is double-bonded to a carbon atom; collectively, these two atoms are called a carbonyl group. The carbon backbone of the glucose molecule can coil up so that an -OH group near the bottom end of the chain attacks the carbonyl carbon and the glucose molecule forms a ring. This ring-shaped structure is the cyclic form of glucose, while the straight chain structure is the linear form. In solution, the cyclic form is by far the more common.
Glucose can form either five-membered or six-membered rings. The six-membered ring is much more common, and in solution the vast majority of glucose molecules are found to have six-membered rings. Since linear and cyclic forms can inter-convert, however, no glucose molecule is ever fixed in the six-membered ring form; it can go back and forth. It does spend most of its time in the six-membered ring form, but the occasional conversion to and from other forms does something interesting to its structure.
You can depict the cyclic form of glucose by drawing a hexagon on a sheet of paper. One atom in the hexagon is an oxygen atom; the other five are carbon atoms. The hexagon has a -CH2-OH group attached to it and four other -OH groups. Each of these five groups can be either above the plane of the ring, generally depicted as a line pointing up, or below it, with a line pointing down. By convention, the oxygen atom in the ring is drawn in the upper-right corner of the hexagon.
Alpha and Beta
The difference between alpha and beta glucose is nothing more than the position of one of the four -OH groups. The carbon to the right of the oxygen atom in the hexagonal ring is called the anomeric carbon. If the -OH group attached to it is below the ring, the molecule is alpha glucose. If the -OH group is above the ring, the molecule is beta glucose. Since the linear and cyclic forms of glucose inter-convert with each other, alpha glucose can turn into beta glucose and vice versa. If you take a sample of pure alpha glucose and put it into water, you'll end up with a sample that is part alpha and part beta glucose.