Origins
To plunge is to sink like lead. The word traces back to Latin plumbum — 'lead', the heavy grey metal — through one of the most evocative metaphor chains in English etymology.
Roman and medieval sailors measured water depth by throwing a lead weight on a marked rope overboard. This act — heaving the lead — became Vulgar Latin *plumbicāre, which Old French turned into plongier, 'to plunge, to sink into'. The image of lead sinking rapidly through water became the word for any sudden, forceful descent.
The same metal gave English several other words. A plumber was originally a worker in lead — Roman water pipes were made of lead (plumbum), which is why the element's chemical symbol is Pb. A plumb line uses a lead weight to find true vertical. To plummet is to fall like lead. The verb plumb, meaning to measure depth ('plumbing the depths'), preserves the nautical origin most directly.
Figurative Development
Perhaps the most elegant descendant is aplomb. French à plomb means 'according to the plumb line' — perfectly vertical, perfectly balanced. A person with aplomb carries themselves with the steady, centred certainty of a lead weight hanging true. Confidence, in this metaphor, is a matter of gravity.
Plunge entered Middle English in the 14th century and quickly shed its technical nautical meaning. You could plunge into battle, plunge a knife, plunge into debt. The speed and violence of lead hitting water transferred to any sudden, committed action.