Hi Cart,
A convex edge is one where the edge curves convexly. Have a look at a spade in a deck of cards: that spade shape is kind-of a convex edge. If you sharpen a knife on a flat stone, for the most part that edge bevel will be flat. By using different methods, you can get a convex edge bevel which is very sharp, holds its edge very well, and is quite durable. Jerry Hossom has been expolring convex edges a lot lately and he thinks that the convexity helps in cutting as well, adding a wedging effect.
Well, that stuff aside, you can easily put a convex edge on a knife with a belt sander. Using the portion above a platen, or removing the platen completely, will allow the belt to flex. Holding a knife edge down, you hold it at a shallow angle and pressit into the belt, and the belt will try to curve under the edge, forming the Convex shape. You can also do this with sandpaper on a mouse pad. the mouse pad will flex and create that convex shape too. If you are really good, you can create a convex edge on a sharpening stone by varying the angle with which you hold your knife. A "shortcut" way to convex an edge is to use many flat bevels. Sharpen the knife at a shallow angle, say 12 degrees per side. Then put on a steeper secondary bevel (say 15 degrees), and then a third edge bevel (say 18 degrees). The second and third edge bevels would be very tiny and would't take more than a few strokes to form. This isn't exactly a convex edge, but it mimics a convex edge somewhat. By far the most common way is using a belt sander. A Delta 1x30 or similar machine is fine for sharpening knives (and lawnmower blades, machetes, axes, etc!).