A sword’s blade can be brought down to the edge in three different styles: flat, hollow, and convex. A flat edge is when the spine is angled down to the cutting edge straight and flat, the standard edge type that is for general use swords, and is right in between the other two edge types.
A hollow, or concave edge is when the spine is brought down to the edge in a concave angle, which means the sword is much sharper because of such shallow angles, though the edge is fairly delicate, so it would be best used to kill cavalrymen or other lightly armored foes by the dozens.
A convex edge is, obviously, where the spine is brought down to the edge in a convex angle. This means that the edge will be pretty dull, though because of the thickness it will not dent or break on impact, making it suitable for fighting against heavily armed and armored foes.
I had found this video off youtube that begins by describing the edge types in detail, in showing how he makes his sword: