Etymology on "egging on"

What is the etymology on "egging on"?

e.g. It was Jack who did it. But Jane was really egging him on.

Does it actually relate to eggs, or is it simply derived from "urging on"?

The etymology of the verb egg (on) is the same as that of edge. It is of Old Norse origin, and once described in particular the sharp edge of a sword. Perhaps those who were egged on were once so encouraged by the threat of laceration.

Robert Hendrickson, Facts on File Encyclopedia of Word and Phrase Origins, fourth edition (2008) has this entry for egg on:

egg on The expression to egg on has nothing to do with hen's eggs or any other kind of eggs. Neither does it derive from Norman invaders pricking Anglo-Saxon prisoners in the buttocks with their ecgs ("the points of their spears") when urging them to move faster, as one old story claims. To egg on is jut a form of the obsolete English verb "to edge": to incite, provoke, encourage, urge on, push someone nearer to the edge. To egg someone meant the same as to edge someone and was used that way until about 1566, when the expression was first lengthened and became to egg on.

John Ayto, Dictionary of Word Origins (1990) has this comment within a longer entry for egg:

Egg 'incite' as in 'egg on', is a Scandinavian borrowing too. It comes from Old Norse eggja, which was a relative or derivative of egg 'edge' (a cousin of English edge).

And Eric Partridge, Origins: A Short Etymological Dictionary of Modern English (1958) has this:

egg (2) to to urge or incite; ME eggen: ON eggja, (lit) to put an egg, or edge, on: [cross reference omitted].

So even though an egg doesn't have any identifiable edges, the egg of egg on is all about provoking someone (or some group of people) to the edge of action.