Originally the cutting side of a sword — from a PIE root meaning 'sharp' that also produced 'acute,' 'acme,' and 'acid.'
The outside limit of an object, area, or surface; the sharpened side of a blade; a quality or factor that gives superiority over rivals.
Old English 'ecg' meant 'the cutting side of a blade, a sword' — it was fundamentally a weapon word. It descends from Proto-Germanic *agjō (blade, edge), from Proto-Indo-European *h₂eḱ- (sharp, pointed), the same root that gave Latin 'aciēs' (sharp edge, battle line), Latin 'acūtus' (sharp, acute), and Greek 'akmḗ' (point, peak). The generalization from 'blade of a weapon' to 'boundary of any surface' happened gradually
In Old English poetry, 'ecg' was a common kenning-element for 'sword' — warriors were called 'ecg-berend' (edge-bearers). The related Old Norse 'eggja' (to egg on) literally meant 'to put an edge on someone' — to sharpen their resolve — which is how English got the phrase 'to egg someone on.'