Emerge comes from Latin ēmergere — 'to rise out of water', from ex- ('out') + mergere ('to plunge'). An emergency is something that has suddenly emerged. Merge, submerge, and immerse are siblings.
To come out from a concealed or enclosed space; to become known or apparent; to come into being.
From Latin ēmergere meaning 'to rise out of, to come forth from', composed of ē- (ex- 'out of') + mergere 'to dip, to plunge, to immerse'. The image is of rising from water — breaking the surface after being submerged. Latin mergere gives us merge (to plunge together), submerge (to plunge under), and immerse (to plunge into). The word entered
An emergency is literally something that has suddenly emerged — burst up from below without warning. The word preserves the Latin image of a diver surfacing unexpectedly. Emerge, merge, submerge, and immerse all descend from the same Latin verb mergere meaning 'to plunge'. To emerge is to un-plunge — to rise from the water you were dipped into.