When glucose forms a ring (think Haworth conformation), carbon one can have its hydroxyl group in one of two conformations: axial (pointing straight down) or equatorial (pointing slightly up). When it is axial, the glucose is alpha. When it is equatorial, it is beta. This doesn't have as much impact on free, monomeric glucose because it can switch back and forth rapidly (though beta is preferred because it is more stable).
When glucose is polymerized into polysaccharides, though, it matters a lot. If alpha glucose is polymerized you get starch, which is soluble and digestible by humans. If you polymerize beta glucose, however, you get tough, undigestable cellulose.