The edge is the sharpened part of the blade that does the cutting. It is formed where the two bevels meet, and it is measured not by how thin the blade is but by the angle those bevels make and how cleanly they intersect.
An edge is sharp when the two bevels meet at a clean line with no flat, rounded or burred zone between them. A blade can be very thin and still be dull if that intersection has been rounded over by wear.
The angle at that intersection is what your sharpening setup controls. Shallower angles cut better and chip sooner. Steeper angles last longer and cut worse. See bevel and micro-bevel.
Plain edge is a single continuous sharpened line. Serrated is a scalloped edge that saws. A combo edge puts both on one blade, serrations at the heel and plain toward the tip.
Which one you want follows from what you cut. Plain for clean, controlled cuts and easy sharpening. Serrated for rope, webbing and anything fibrous that a plain edge slides off.