A swedge is a section of a knife's spine, beginning at the point and extending generally one-third to one-half the length of the blade, which has been ground to give the appearance of a second edge (but without actually being sharpened).
The purpose of a swedge is, in most cases, purely decorative. Properly made, however, a swedged blade can perform certain tasks -- plunge cuts, for example, and thrusts -- more efficiently.
A decorative swedge can be sharpened, effectively creating a double-edged blade. Before buying a knife with a sharpened swedge (or sharpening an unsharpened swedge), check your local and state laws regulating possession of double-edged blades.