The word 'storm' descends from Old English 'storm' (a tempest, a violent disturbance of the atmosphere), from Proto-Germanic *sturmaz (storm, tumult, noise), possibly from PIE *(s)tur- or *stwer- (to turn, to whirl, to rotate). If this etymology is correct, the fundamental image behind 'storm' is of air in violent circular motion — whirling, churning, turbulent — which is a remarkably accurate description of the actual meteorological phenomenon.
The Proto-Germanic cognates are consistent: German 'Sturm,' Dutch 'storm,' Old Norse 'stormr,' Swedish 'storm,' Danish 'storm,' and Old High German 'sturm.' The word appears in all Germanic branches with essentially the same meaning, suggesting it was firmly established in Proto-Germanic. From the beginning, it carried both a literal meteorological sense and a figurative sense of violent commotion or assault.
The possible PIE connection to *(s)tur- (to whirl) would make 'storm' a distant relative of Latin 'turba' (crowd, confusion, turmoil) and 'turbāre' (to disturb, to throw into disorder). From these Latin words, English acquired 'turbulent' (violently agitated), 'turbine' (a rotating engine), 'disturb' (to throw into disorder), 'perturb' (to unsettle), and — through Old French — 'trouble' (from Vulgar Latin *turbulāre, to make turbid). The mobile s- at the beginning (present in Germanic *sturmaz but absent in Latin 'turba') is a known PIE phenomenon called s-mobile, where an initial s- could optionally attach to certain roots.
The military sense of 'storm' — to assault a fortified position with sudden violence — dates from the medieval period. 'To take by storm' originally meant to capture a castle or city by direct, overwhelming assault rather than by siege. The metaphorical extension to any overwhelming success ('she took Broadway by storm') came later, in the 19th century.
German 'Sturm und Drang' (Storm and Stress), the literary movement of the 1770s–1780s, took its name from a play by Friedrich Maximilian Klinger. The movement, whose most famous figures were the young Goethe and Schiller, celebrated raw emotion, individualism, and nature's power over Enlightenment rationalism. The phrase has entered English as a general term for a period of emotional turmoil.
The compound-forming productivity of 'storm' in English is remarkable: thunderstorm, snowstorm, rainstorm, hailstorm, firestorm, sandstorm, brainstorm, barnstorm, ice storm. Each compound specifies the type of violent atmospheric event or extends the metaphor of sudden, overwhelming force to non-meteorological contexts. 'Brainstorm' (a sudden burst of ideas) dates from the 1890s. 'Firestorm' (a conflagration intensified by its own updraft) was coined during World War II to describe the devastation of aerial bombing.