Old English seoþan "to boil," also figuratively, "be troubled in mind, brood" (class II strong verb; past tense seaþ, past participle soden), from Proto-Germanic *seuthan (source also of Old Norse sjoða, Old Frisian siatha, Dutch zieden, Old High German siodan, German sieden "to seethe"), from PIE root *seut- "to seethe, boil."
Driven out of its literal meaning by boil (v.); it survives largely in metaphoric extensions. Figurative use, of persons or populations, "to be in a state of inward agitation" is recorded from 1580s (implied in seething). It had wider figurative uses in Old English, such as "to try by fire, to afflict with cares." Now conjugated as a weak verb, and past participle sodden (q.v.) is no longer felt as connected.