Old English swimman "to move in or on the water, float" (class III strong verb; past tense swamm, past participle swummen), from Proto-Germanic *swemjanan (cf. Old Saxon and Old High German swimman, Old Norse svimma, Dutch zwemmen, German schwimmen), from PIE root *swem- "to be in motion."
The root is sometimes said to be restricted to Germanic, but possible cognates are Welsh chwyf "motion," Old Irish do-sennaim "I hunt," Lithuanian sundyti "to chase." For the usual Indo-European word, see natatorium. Sense of "reel or move unsteadily" first recorded 1670s; of the head or brain, from 1702. Figurative phrase sink or swim is attested from mid-15c., often with reference to ordeals of suspected witches.
1540s, "the clear part of any liquid" (above the sediment), from swim (v.). Meaning "part of a river or stream frequented by fish" (and hence fishermen) is from 1828, and is probably the source of the figurative meaning "the current of the latest affairs or events" (1869).